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example-inc-output.mw
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<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="11" minor="1"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="true"><Zoom percentage="75"/></View-Properties>
<MapleNet-Properties warnlevel="3" longdelim="true" plotoptions="" echo="1" errorcursor="false" elisiontermsthreshold="10000" elisiontermsbefore="100" errorbreak="1" prettyprint="3" prompt="> " latexwidth="6.0" useclientjvm="true" ansi="false" screenheight="25" labelwidth="20" plotdevice="inline" typesetting="standard" displayprecision="-1" indentamount="4" elisiondigitsthreshold="10000" quiet="false" plotoutput="terminal" rtablesize="10" preplot="" showassumed="1" plotdriver="openviz" elisiontermsafter="100" labelling="true" postplot="" screenwidth="79" elisiondigitsbefore="100" elisiondigitsafter="100" verboseproc="1" imaginaryunit="I" ShowLabels="true"/>
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<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
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<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
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<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
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<Text-field style="Heading 1" layout="Heading 1">load linear algebra package</Text-field></Title>
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<Text-field prompt="> " style="Maple Input" layout="Normal">with(CodeGeneration):</Text-field>
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<Text-field prompt="> " style="Maple Input" layout="Normal">with(LinearAlgebra):</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Heading 1" layout="Heading 1">Transformation matrices for tower middle</Text-field></Title><Presentation-Block>
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<Text-field prompt="> " style="Maple Input" layout="Normal">R[rho] := Matrix([[cos(rho),0,-sin(rho)],[0,1,0],[sin(rho),0,cos(rho)]]);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlJHNiI2I0kkcmhvR0YlLUknUlRBQkxFR0YlNiUiKjdYZV8iLUknTUFUUklYR0YlNiM3JTclLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlRiYiIiEsJC1JJHNpbkdGM0YmISIiNyVGNiIiIkY2NyVGOEY2RjFJJ01hdHJpeEdGMw==">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</Equation></Text-field>
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<Text-field style="Heading 1" layout="Heading 1">Transformation matrices for blade 1</Text-field></Title><Presentation-Block>
<Group view="code" hide-input="true" hide-output="false" inline-output="false" labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R[psi[1]] := Matrix([[-cos(psi),sin(psi),0],[-sin(psi),-cos(psi),0],[0,0,1]]);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlJHNiI2IyZJJHBzaUdGJTYjIiIiLUknUlRBQkxFR0YlNiUiKls2WmAiLUknTUFUUklYR0YlNiM3JTclLCQtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0YoISIiLUkkc2luR0Y3RjoiIiE3JSwkRjxGO0Y0Rj43JUY+Rj5GKkknTWF0cml4R0Y3">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</Equation></Text-field>
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<Text-field prompt="> " style="Maple Input" layout="Normal">R[beta[1]] := Matrix([[cos(beta[1]),0,-sin(beta[1])],[0,1,0],[sin(beta[1]),0,cos(beta[1])]]);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlJHNiI2IyZJJWJldGFHRiU2IyIiIi1JJ1JUQUJMRUdGJTYlIipnOVtgIi1JJ01BVFJJWEdGJTYjNyU3JS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUYmIiIhLCQtSSRzaW5HRjZGJiEiIjclRjlGKkY5NyVGO0Y5RjRJJ01hdHJpeEdGNg==">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</Equation></Text-field>
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<Text-field style="Heading 1" layout="Heading 1">Transformation matrices for blade 2</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R[psi[2]] := Matrix([[cos(psi),-sin(psi),0],[sin(psi),cos(psi),0],[0,0,1]]);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlJHNiI2IyZJJHBzaUdGJTYjIiIjLUknUlRBQkxFR0YlNiUiKmsjKltgIi1JJ01BVFJJWEdGJTYjNyU3JS1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjRigsJC1JJHNpbkdGNkY5ISIiIiIhNyVGO0Y0Rj43JUY+Rj4iIiJJJ01hdHJpeEdGNg==">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</Equation></Text-field>
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<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R[beta[2]] := Matrix([[cos(beta[2]),0,-sin(beta[2])],[0,1,0],[sin(beta[2]),0,cos(beta[2])]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIlJHNiI2IyZJJWJldGFHRiU2IyIiIy1JJ1JUQUJMRUdGJTYlIipnJypcYCItSSdNQVRSSVhHRiU2IzclNyUtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiVGJiIiISwkLUkkc2luR0Y2RiYhIiI3JUY5IiIiRjk3JUY7RjlGNEknTWF0cml4R0Y2">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</Equation></Text-field>
</Output>
</Group></Presentation-Block>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">omega of blade 1, in function of {E_beta_1}</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L38" drawlabel="true">
<Input>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">omega of the tower, in function of {E_1}</Text-field></Title>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[rho] := Vector[row]([0,rho[flux],0]);</Text-field>
</Section>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiNJJHJob0dGJS1JJ1JUQUJMRUdGJTYlIipzNj9fIi1JJ1ZFQ1RPUkdGJTYjNyUiIiEmRic2I0klZmx1eEdGJUYwJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJJHJvd0dGJQ==">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[rho[1]] := Multiply(omega[rho],Multiply(Transpose(R[psi[1]]),Transpose(R[beta[1]])));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiMmSSRyaG9HRiU2IyIiIi1JJ1JUQUJMRUdGJTYlIio3Sz9fIi1JJ1ZFQ1RPUkdGJTYjNyUqKCZGKDYjSSVmbHV4R0YlRiotSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0kkcHNpR0YlRiotSSRjb3NHRjk2IyZJJWJldGFHRiVGKUYqLCQqJkY0RiotRj9GPEYqISIiKihGNEYqRjdGKi1GOEZARiomSSdWZWN0b3JHRjk2I0kkcm93R0Yl">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[Omega[1]] := Multiply(Vector[row]([0,0,-Omega]),Transpose(R[beta[1]]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiMmSSZPbWVnYUdGJTYjIiIiLUknUlRBQkxFR0YlNiUiKjdNP18iLUknVkVDVE9SR0YlNiM3JSomRihGKi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjJkklYmV0YUdGJUYpRioiIiEsJComRihGKi1JJGNvc0dGNkY5RiohIiImSSdWZWN0b3JHRjY2I0kkcm93R0Yl">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[beta[1]] := Vector[row]([0,beta[flux[1]],0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiMmSSViZXRhR0YlNiMiIiItSSdSVEFCTEVHRiU2JSIqc04/XyItSSdWRUNUT1JHRiU2IzclIiIhJkYoNiMmSSVmbHV4R0YlRilGMyZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRyb3dHRiU=">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[1] := VectorAdd(VectorAdd(omega[rho[1]],omega[Omega[1]]), omega[beta[1]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiMiIiItSSdSVEFCTEVHRiU2JSIqN2p1YCItSSdWRUNUT1JHRiU2IzclLCYqKCZJJHJob0dGJTYjSSVmbHV4R0YlRictSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0kkcHNpR0YlRictSSRjb3NHRjg2IyZJJWJldGFHRiVGJkYnRicqJkkmT21lZ2FHRiVGJy1GN0Y/RidGJywmKiZGMkYnLUY+RjtGJyEiIiZGQTYjJkY1RiZGJywmKihGMkYnRjZGJ0ZERidGJyomRkNGJ0Y9RidGSCZJJ1ZlY3RvckdGODYjSSRyb3dHRiU=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUkjbW5HRiQ2JFEiMUYnRjUvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRjRGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWi1JKG1hY3Rpb25HRiQ2JS1JKG1mZW5jZWRHRiQ2KC1JJ210YWJsZUdGJDY1LUkkbXRyR0YkNigtSSRtdGRHRiQ2KC1GIzYoLUYjNiotRiw2JS1GLzYlUScmIzk2MTtGJ0YyRjUtRiM2Ji1GLzYlUSVmbHV4RicvRjNRJXRydWVGJy9GNlEnaXRhbGljRidGPkZBRjVGQy1GRzYtUTEmSW52aXNpYmxlVGltZXM7RidGNUZKRkxGTkZQRlJGVEZWL0ZZUSYwLjBlbUYnL0ZmbkZccS1GIzYoLUYvNiVRJHNpbkYnRjJGNS1GRzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y1RkpGTEZORlBGUkZURlZGW3FGXXEtRltvNiQtRiM2Ji1GLzYlUScmIzk2ODtGJ0YyRjVGPkZBRjVGNUY+RkFGNUZocC1GIzYoLUYvNiVRJGNvc0YnRjJGNUZjcS1GW282JC1GIzYmLUYsNiUtRi82JVEnJiM5NDY7RidGMkY1RjhGQ0Y+RkFGNUY1Rj5GQUY1Rj5GQUY1LUZHNi1RIitGJ0Y1RkpGTEZORlBGUkZURlYvRllRLDAuMjIyMjIyMmVtRicvRmZuRl9zLUYjNigtRi82JVEnJiM5Mzc7RidGMkY1RmhwLUYjNihGYHFGY3FGYnJGPkZBRjVGPkZBRjVGPkZBRjUvJSlyb3dhbGlnbkdRIUYnLyUsY29sdW1uYWxpZ25HRmpzLyUrZ3JvdXBhbGlnbkdGanMvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGYXQtRmRvNigtRiM2KS1GRzYtUSomdW1pbnVzMDtGJ0Y1RkpGTEZORlBGUkZURlZGXnNGYHMtRiM2KEZqb0ZocC1GIzYoRl9yRmNxRmZxRj5GQUY1Rj5GQUY1RltzLUYsNiVGaHItRiM2Ji1GLDYlRmFwRjhGQ0Y+RkFGNUZDRj5GQUY1RmhzRlt0Rl10Rl90RmJ0LUZkbzYoLUYjNigtRiM2KkZqb0ZocEZecUZocEZmc0Y+RkFGNS1GRzYtUSgmbWludXM7RidGNUZKRkxGTkZQRlJGVEZWRl5zRmBzLUYjNihGY3NGaHBGXXJGPkZBRjVGPkZBRjVGaHNGW3RGXXRGX3RGYnRGaHNGW3RGXXQvJSZhbGlnbkdRJWF4aXNGJy9GaXNRKWJhc2VsaW5lRicvRlx0USdjZW50ZXJGJy9GXnRRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0ZlcC8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRl13LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmh3LyUmZnJhbWVHRmh3LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGNC8lLWVxdWFsY29sdW1uc0dGNC8lLWRpc3BsYXlzdHlsZUdGNC8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0Zld0Y1L0krbXNlbWFudGljc0dGJFEqUm93VmVjdG9yRicvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGW3kvJSthY3Rpb250eXBlR1EucnRhYmxlYWRkcmVzc0YnLyUpcnRhYmxlaWRHUSoxNTE4OTQzNzZGJ0Y+RkFGNQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L220" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">p_omega[1]:=omega[1][1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJKHBfb21lZ2FHNiI2IyIiIiwmKigmSSRyaG9HRiU2I0klZmx1eEdGJUYnLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJJHBzaUdGJUYnLUkkY29zR0YwNiMmSSViZXRhR0YlRiZGJ0YnKiZJJk9tZWdhR0YlRictRi9GN0YnRic=">LCYqKCZJJHJob0c2IjYjSSVmbHV4R0YmIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNJJHBzaUdGJkYpLUkkY29zR0YsNiMmSSViZXRhR0YmNiNGKUYpRikqJkkmT21lZ2FHRiZGKS1GK0YzRilGKQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L221" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">q_omega[1]:=omega[1][2];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJKHFfb21lZ2FHNiI2IyIiIiwmKiYmSSRyaG9HRiU2I0klZmx1eEdGJUYnLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJJHBzaUdGJUYnISIiJkklYmV0YUdGJTYjJkYtRiZGJw==">LCYqJiZJJHJob0c2IjYjSSVmbHV4R0YmIiIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNJJHBzaUdGJkYpISIiJkklYmV0YUdGJjYjJkYoNiNGKUYp</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L222" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_omega[1]:=omega[1][3];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJKHJfb21lZ2FHNiI2IyIiIiwmKigmSSRyaG9HRiU2I0klZmx1eEdGJUYnLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJJHBzaUdGJUYnLUYvNiMmSSViZXRhR0YlRiZGJ0YnKiZJJk9tZWdhR0YlRictSSRjb3NHRjBGNkYnISIi">LCYqKCZJJHJob0c2IjYjSSVmbHV4R0YmIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNJJHBzaUdGJkYpLUYrNiMmSSViZXRhR0YmNiNGKUYpRikqJkkmT21lZ2FHRiZGKS1JJGNvc0dGLEYyRikhIiI=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L555" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">omega of blade 2, in function of {E_beta_2}</Text-field></Title><Presentation-Block>
<Group view="code" labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[rho[2]] := Multiply(omega[rho],Multiply(Transpose(R[psi[2]]),Transpose(R[beta[2]])));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiMmSSRyaG9HRiU2IyIiIy1JJ1JUQUJMRUdGJTYlIipfRXRgIi1JJ1ZFQ1RPUkdGJTYjNyUsJCooJkYoNiNJJWZsdXhHRiUiIiItSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2I0kkcHNpR0YlRjgtSSRjb3NHRjs2IyZJJWJldGFHRiVGKUY4ISIiKiZGNUY4LUZBRj5GOCwkKihGNUY4RjlGOC1GOkZCRjhGRSZJJ1ZlY3RvckdGOzYjSSRyb3dHRiU=">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[Omega[2]] := Multiply(Vector[row]([0,0,-Omega]),Transpose(R[beta[2]]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiMmSSZPbWVnYUdGJTYjIiIjLUknUlRBQkxFR0YlNiUiKjdJP18iLUknVkVDVE9SR0YlNiM3JSomRigiIiItSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyZJJWJldGFHRiVGKUY0IiIhLCQqJkYoRjQtSSRjb3NHRjdGOkY0ISIiJkknVmVjdG9yR0Y3NiNJJHJvd0dGJQ==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[beta[2]] := Vector[row]([0,beta[flux[2]],0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiMmSSViZXRhR0YlNiMiIiMtSSdSVEFCTEVHRiU2JSIqN0U/XyItSSdWRUNUT1JHRiU2IzclIiIhJkYoNiMmSSVmbHV4R0YlRilGMyZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRyb3dHRiU=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUYsNiUtRi82JVEnJiM5NDY7RidGMkY1LUYjNiYtSSNtbkdGJDYkUSIyRidGNS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGNEY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGRUZIRjVGSi1JI21vR0YkNi1RIzo9RidGNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRltvLUkobWFjdGlvbkdGJDYlLUkobWZlbmNlZEdGJDYoLUknbXRhYmxlR0YkNjUtSSRtdHJHRiQ2KC1JJG10ZEdGJDYoLUZCNiRRIjBGJ0Y1LyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0ZicC8lK2dyb3VwYWxpZ25HRmJwLyUocm93c3BhbkdRIjFGJy8lK2NvbHVtbnNwYW5HRmlwLUZbcDYoLUYsNiVGPC1GIzYmLUYsNiUtRi82JVElZmx1eEYnL0YzUSV0cnVlRicvRjZRJ2l0YWxpY0YnRj9GSkZFRkhGNUZKRmBwRmNwRmVwRmdwRmpwRmpvRmBwRmNwRmVwLyUmYWxpZ25HUSVheGlzRicvRmFwUSliYXNlbGluZUYnL0ZkcFEnY2VudGVyRicvRmZwUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGaHEvJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0Zoci8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0Zjcy8lJmZyYW1lR0Zjcy8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRjQvJS1lcXVhbGNvbHVtbnNHRjQvJS1kaXNwbGF5c3R5bGVHRjQvJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dGYHNGNS9JK21zZW1hbnRpY3NHRiRRKlJvd1ZlY3RvckYnLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmZ0LyUrYWN0aW9udHlwZUdRLnJ0YWJsZWFkZHJlc3NGJy8lKXJ0YWJsZWlkR1EqMTUxOTA4NjQwRidGRUZIRjU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">omega[2] := VectorAdd(VectorAdd(omega[rho[2]],omega[Omega[2]]), omega[beta[2]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJm9tZWdhRzYiNiMiIiMtSSdSVEFCTEVHRiU2JSIqIzQsQTotSSdWRUNUT1JHRiU2IzclLCYqKCZJJHJob0dGJTYjSSVmbHV4R0YlIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJJHBzaUdGJUY2LUkkY29zR0Y5NiMmSSViZXRhR0YlRiZGNiEiIiomSSZPbWVnYUdGJUY2LUY4RkBGNkY2LCYqJkYyRjYtRj9GPEY2RjYmRkI2IyZGNUYmRjYsJiooRjJGNkY3RjZGRkY2RkMqJkZFRjZGPkY2RkMmSSdWZWN0b3JHRjk2I0kkcm93R0Yl">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L223" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">p_omega[2]:=omega[2][1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJKHBfb21lZ2FHNiI2IyIiIywmKigmSSRyaG9HRiU2I0klZmx1eEdGJSIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRwc2lHRiVGLi1JJGNvc0dGMTYjJkklYmV0YUdGJUYmRi4hIiIqJkkmT21lZ2FHRiVGLi1GMEY4Ri5GLg==">LCYqKCZJJHJob0c2IjYjSSVmbHV4R0YmIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNJJHBzaUdGJkYpLUkkY29zR0YsNiMmSSViZXRhR0YmNiMiIiNGKSEiIiomSSZPbWVnYUdGJkYpLUYrRjNGKUYp</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L224" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">q_omega[2]:=omega[2][2];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJKHFfb21lZ2FHNiI2IyIiIywmKiYmSSRyaG9HRiU2I0klZmx1eEdGJSIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRwc2lHRiVGLkYuJkklYmV0YUdGJTYjJkYtRiZGLg==">LCYqJiZJJHJob0c2IjYjSSVmbHV4R0YmIiIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNJJHBzaUdGJkYpRikmSSViZXRhR0YmNiMmRig2IyIiI0Yp</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L225" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_omega[2]:=omega[2][3];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJKHJfb21lZ2FHNiI2IyIiIywmKigmSSRyaG9HRiU2I0klZmx1eEdGJSIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRwc2lHRiVGLi1GMDYjJkklYmV0YUdGJUYmRi4hIiIqJkkmT21lZ2FHRiVGLi1JJGNvc0dGMUY3Ri5GOg==">LCYqKCZJJHJob0c2IjYjSSVmbHV4R0YmIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiNJJHBzaUdGJkYpLUYrNiMmSSViZXRhR0YmNiMiIiNGKSEiIiomSSZPbWVnYUdGJkYpLUkkY29zR0YsRjJGKUY3</Equation></Text-field>
</Output>
</Group></Presentation-Block>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">rotation operators</Text-field></Title>
<Group labelreference="L227" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Omega[Xomega[rho]]:=Matrix([[0,0,-rho[flux]],[0,0,0],[rho[flux],0,0]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJk9tZWdhRzYiNiMmSSdYb21lZ2FHRiU2I0kkcmhvR0YlLUknUlRBQkxFR0YlNiUiKi8iUVM7LUknTUFUUklYR0YlNiM3JTclIiIhRjQsJCZGKjYjSSVmbHV4R0YlISIiNyVGNEY0RjQ3JUY2RjRGNEknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0Yl">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L237" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Omega[Xomega[1]]:=Matrix([[0,r_omega[1],-q_omega[1]],[-r_omega[1],0,p_omega[1]],[q_omega[1],-p_omega[1],0]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJk9tZWdhRzYiNiMmSSdYb21lZ2FHRiU2IyIiIi1JJ1JUQUJMRUdGJTYlIipnYC9rIi1JJ01BVFJJWEdGJTYjNyU3JSIiISwmKigmSSRyaG9HRiU2I0klZmx1eEdGJUYqLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJJHBzaUdGJUYqLUY8NiMmSSViZXRhR0YlRilGKkYqKiZGJEYqLUkkY29zR0Y9RkNGKiEiIiwmKiZGN0YqLUZIRkBGKkYqJkZFNiMmRjpGKUZJNyUsJkY2RklGRkYqRjQsJiooRjdGKkY7RipGR0YqRioqJkYkRipGQkYqRio3JSwmRktGSUZNRiosJkZTRklGVEZJRjRJJ01hdHJpeEdGPQ==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L238" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">Omega[Xomega[2]]:=Matrix([[0,r_omega[2],-q_omega[2]],[-r_omega[2],0,p_omega[2]],[q_omega[2],-p_omega[2],0]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJk9tZWdhRzYiNiMmSSdYb21lZ2FHRiU2IyIiIy1JJ1JUQUJMRUdGJTYlIiohPWNTOy1JJ01BVFJJWEdGJTYjNyU3JSIiISwmKigmSSRyaG9HRiU2I0klZmx1eEdGJSIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRwc2lHRiVGOy1GPTYjJkklYmV0YUdGJUYpRjshIiIqJkYkRjstSSRjb3NHRj5GREY7RkcsJiomRjdGOy1GSkZBRjtGRyZGRjYjJkY6RilGRzclLCZGNkY7RkhGO0Y0LCYqKEY3RjtGPEY7RklGO0ZHKiZGJEY7RkNGO0Y7NyUsJkZMRjtGTkY7LCZGVEY7RlVGR0Y0SSdNYXRyaXhHRj4=">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</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Position vectors for the cg of the blades and the cg of the 2nd tower section</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L278" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">All captial R position vectors here are expressed in {E_1}</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L413" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">all r position vectors are in local reference frame</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L243" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_2 := Vector[row]([l/2,0,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkcl8yRzYiLUknUlRBQkxFR0YkNiUiKnNkJ0c6LUknVkVDVE9SR0YkNiM3JSwkKiYjIiIiIiIjRjBJImxHRiRGMEYwIiIhRjMmSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcm93R0Yk">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L245" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_0 := Vector[row]([l/2,0,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkcl8wRzYiLUknUlRBQkxFR0YkNiUiKkMkPUE6LUknVkVDVE9SR0YkNiM3JSwkKiYjIiIiIiIjRjBJImxHRiRGMEYwIiIhRjMmSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcm93R0Yk">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L246" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_cg_beta := Vector[row]([R/2,0,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkqcl9jZ19iZXRhRzYiLUknUlRBQkxFR0YkNiUiKkMrQ18iLUknVkVDVE9SR0YkNiM3JSwkKiYjIiIiIiIjRjBJIlJHRiRGMEYwIiIhRjMmSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcm93R0Yk">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L247" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_cg_T := Vector[row]([l/4,0,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkncl9jZ19URzYiLUknUlRBQkxFR0YkNiUiKl8zP18iLUknVkVDVE9SR0YkNiM3JSwkKiYjIiIiIiIlRjBJImxHRiRGMEYwIiIhRjMmSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcm93R0Yk">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L622" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_3_beta_1 := Vector[row]([(-e*cos(psi)),(e*sin(psi)),0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkrcl8zX2JldGFfMUc2Ii1JJ1JUQUJMRUdGJDYlIiojZk5TOy1JJ1ZFQ1RPUkdGJDYjNyUsJComSSJlR0YkIiIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHBzaUdGJEYwISIiKiZGL0YwLUkkc2luR0YzRjZGMCIiISZJJ1ZlY3RvckdGMzYjSSRyb3dHRiQ=">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L623" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_3_beta_2 := Vector[row]([(e*cos(psi)),(-e*sin(psi)),0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkrcl8zX2JldGFfMkc2Ii1JJ1JUQUJMRUdGJDYlIipfNT9fIi1JJ1ZFQ1RPUkdGJDYjNyUqJkkiZUdGJCIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSRwc2lHRiRGLywkKiZGLkYvLUkkc2luR0YyRjVGLyEiIiIiISZJJ1ZlY3RvckdGMjYjSSRyb3dHRiQ=">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L624" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_3_beta_1_flux := Vector[row]([(e*sin(psi)*psi[flux]),(e*cos(psi)*psi[flux]),0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkwcl8zX2JldGFfMV9mbHV4RzYiLUknUlRBQkxFR0YkNiUiKjc3P18iLUknVkVDVE9SR0YkNiM3JSooSSJlR0YkIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHBzaUdGJEYvJkY2NiNJJWZsdXhHRiRGLyooRi5GLy1JJGNvc0dGMkY1Ri9GN0YvIiIhJkknVmVjdG9yR0YyNiNJJHJvd0dGJA==">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L625" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">r_3_beta_2_flux := Vector[row]([(-e*sin(psi)*psi[flux]),(-e*cos(psi)*psi[flux]),0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkwcl8zX2JldGFfMl9mbHV4RzYiLUknUlRBQkxFR0YkNiUiKk8qUk86LUknVkVDVE9SR0YkNiM3JSwkKihJImVHRiQiIiItSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcHNpR0YkRjAmRjc2I0klZmx1eEdGJEYwISIiLCQqKEYvRjAtSSRjb3NHRjNGNkYwRjhGMEY7IiIhJkknVmVjdG9yR0YzNiNJJHJvd0dGJA==">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L248" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_beta_1 := Multiply(r_0,Transpose(R[rho])) + r_2 + r_3_beta_1 + Multiply(r_cg_beta,Multiply(R[beta[1]],R[psi[1]]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkksUl9jZ19iZXRhXzFHNiItSSdSVEFCTEVHRiQ2JSIqRzMnRzotSSdWRUNUT1JHRiQ2IzclLCoqKCMiIiIiIiNGMEkibEdGJEYwLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHJob0dGJEYwRjAqJkYvRjBGMkYwRjAqJkkiZUdGJEYwLUY0NiNJJHBzaUdGJEYwISIiKipGL0YwSSJSR0YkRjBGPUYwLUY0NiMmSSViZXRhR0YkNiNGMEYwRkAsJiomRjxGMC1JJHNpbkdGNUY+RjBGMCoqRi9GMEZCRjBGSkYwRkNGMEYwLCYqKEYvRjBGMkYwLUZLRjhGMEYwKihGL0YwRkJGMC1GS0ZERjBGQCZJJ1ZlY3RvckdGNTYjSSRyb3dHRiQ=">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L249" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_beta_2 := Multiply(r_0,Transpose(R[rho])) + r_2 + r_3_beta_2 + Multiply(r_cg_beta,Multiply(R[beta[2]],R[psi[2]]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkksUl9jZ19iZXRhXzJHNiItSSdSVEFCTEVHRiQ2JSIqJW8vUzstSSdWRUNUT1JHRiQ2IzclLCoqKCMiIiIiIiNGMEkibEdGJEYwLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHJob0dGJEYwRjAqJkYvRjBGMkYwRjAqJkkiZUdGJEYwLUY0NiNJJHBzaUdGJEYwRjAqKkYvRjBJIlJHRiRGMEY9RjAtRjQ2IyZJJWJldGFHRiQ2I0YxRjBGMCwmKiZGPEYwLUkkc2luR0Y1Rj5GMCEiIioqRi9GMEZBRjBGSUYwRkJGMEZLLCYqKEYvRjBGMkYwLUZKRjhGMEYwKihGL0YwRkFGMC1GSkZDRjBGSyZJJ1ZlY3RvckdGNTYjSSRyb3dHRiQ=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEsUl9jZ19iZXRhXzJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWFjdGlvbkdGJDYlLUkobWZlbmNlZEdGJDYoLUknbXRhYmxlR0YkNjUtSSRtdHJHRiQ2KC1JJG10ZEdGJDYoLUYjNiwtRiM2KC1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGOS1GYG82JFEiMkYnRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRltwLyUpYmV2ZWxsZWRHRj0tRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZkcC1GIzYoLUYsNiVRImxGJ0YvRjJGYHAtRiM2KC1GLDYlUSRjb3NGJy9GMEY9RjktRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRmNwRmVwLUZTNiQtRiM2Ji1GLDYlUScmIzk2MTtGJ0ZgcUY5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9RjlGOUZbckZeckY5RltyRl5yRjlGW3JGXnJGOS1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmRyLUYjNihGXG9GYHAtRiM2JkZocEZbckZeckY5RltyRl5yRjlGYHItRiM2KC1GLDYlUSJlRidGL0YyRmBwLUYjNihGXXFGYXEtRlM2JC1GIzYmLUYsNiVRJyYjOTY4O0YnRmBxRjlGW3JGXnJGOUY5RltyRl5yRjlGW3JGXnJGOUZgci1GIzYoRlxvRmBwLUYjNiotRiw2JVEiUkYnRi9GMkZgcEZfc0ZgcC1GIzYoRl1xRmFxLUZTNiQtRiM2Ji1JJW1zdWJHRiQ2JS1GLDYlUScmIzk0NjtGJ0ZgcUY5LUYjNiZGY29GW3JGXnJGOS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRltyRl5yRjlGOUZbckZeckY5RltyRl5yRjlGW3JGXnJGOUZbckZeckY5LyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0ZidS8lK2dyb3VwYWxpZ25HRmJ1LyUocm93c3BhbkdGaG8vJStjb2x1bW5zcGFuR0Zoby1GZm42KC1GIzYpLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSEZjckZlci1GIzYoRlxzRmBwLUYjNigtRiw2JVEkc2luRidGYHFGOUZhcUZhc0ZbckZeckY5RltyRl5yRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSEZjckZlci1GIzYoRlxvRmBwLUYjNipGXHRGYHBGZHZGYHBGX3RGW3JGXnJGOUZbckZeckY5RltyRl5yRjlGYHVGY3VGZXVGZ3VGaXUtRmZuNigtRiM2KC1GIzYoRlxvRmBwLUYjNihGaHBGYHAtRiM2KEZmdkZhcUZkcUZbckZeckY5RltyRl5yRjlGW3JGXnJGOUZpdi1GIzYoRlxvRmBwLUYjNihGXHRGYHAtRiM2KEZmdkZhcUZhdEZbckZeckY5RltyRl5yRjlGW3JGXnJGOUZbckZeckY5RmB1RmN1RmV1Rmd1Rml1RmB1RmN1RmV1LyUmYWxpZ25HUSVheGlzRicvRmF1USliYXNlbGluZUYnL0ZkdUZbcC9GZnVRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0YxLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGXHkvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGZ3kvJSZmcmFtZUdGZ3kvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0Y9LyUtZXF1YWxjb2x1bW5zR0Y9LyUtZGlzcGxheXN0eWxlR0Y9LyUlc2lkZUdRJnJpZ2h0RicvJTBtaW5sYWJlbHNwYWNpbmdHRmR5RjkvSSttc2VtYW50aWNzR0YkUSpSb3dWZWN0b3JGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zqei8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRKjE1MDUyMDY1NkYnRltyRl5yRjk=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L256" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_T := Multiply(r_0,Transpose(R[rho])) + r_cg_T;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknUl9jZ19URzYiLUknUlRBQkxFR0YkNiUiKicqeilHOi1JJ1ZFQ1RPUkdGJDYjNyUsJiooIyIiIiIiI0YwSSJsR0YkRjAtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcmhvR0YkRjBGMComI0YwIiIlRjBGMkYwRjAiIiEsJCooRi9GMEYyRjAtSSRzaW5HRjVGOEYwRjAmSSdWZWN0b3JHRjU2I0kkcm93R0Yk">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnUl9jZ19URicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JKG1hY3Rpb25HRiQ2JS1JKG1mZW5jZWRHRiQ2KC1JJ210YWJsZUdGJDY1LUkkbXRyR0YkNigtSSRtdGRHRiQ2KC1GIzYoLUYjNigtSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JFEiMUYnRjktRmBvNiRRIjJGJ0Y5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZbcC8lKWJldmVsbGVkR0Y9LUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZHAtRiM2KC1GLDYlUSJsRidGL0YyRmBwLUYjNigtRiw2JVEkY29zRicvRjBGPUY5LUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZjcEZlcC1GUzYkLUYjNiYtRiw2JVEnJiM5NjE7RidGYHFGOS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5RjlGW3JGXnJGOUZbckZeckY5RltyRl5yRjktRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZkci1GIzYoLUZdbzYoRl9vLUZgbzYkUSI0RidGOUZmb0Zpb0ZccEZecEZgcC1GIzYmRmhwRltyRl5yRjlGW3JGXnJGOUZbckZeckY5LyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0Zhcy8lK2dyb3VwYWxpZ25HRmFzLyUocm93c3BhbkdGaG8vJStjb2x1bW5zcGFuR0Zoby1GZm42KC1GYG82JFEiMEYnRjlGX3NGYnNGZHNGZnNGaHMtRmZuNigtRiM2KEZcb0ZgcC1GIzYoRmhwRmBwLUYjNigtRiw2JVEkc2luRidGYHFGOUZhcUZkcUZbckZeckY5RltyRl5yRjlGW3JGXnJGOUZfc0Zic0Zkc0Zmc0Zoc0Zfc0Zic0Zkcy8lJmFsaWduR1ElYXhpc0YnL0Zgc1EpYmFzZWxpbmVGJy9GY3NGW3AvRmVzUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGMS8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmZ1LyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmF2LyUmZnJhbWVHRmF2LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGPS8lLWVxdWFsY29sdW1uc0dGPS8lLWRpc3BsYXlzdHlsZUdGPS8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZedkY5L0krbXNlbWFudGljc0dGJFEqUm93VmVjdG9yRicvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZHcvJSthY3Rpb250eXBlR1EucnRhYmxlYWRkcmVzc0YnLyUpcnRhYmxlaWRHUSoxNTE4OTUwNzJGJ0ZbckZeckY5</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L252" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_beta_1_flux := Multiply(r_2,Omega[Xomega[rho]]) + Multiply(r_3_beta_1,Omega[Xomega[rho]]) + r_3_beta_1_flux + Multiply(r_cg_beta,Multiply(Omega[Xomega[1]],Multiply(R[beta[1]],R[psi[1]])));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L253" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_beta_2_flux := Multiply(r_2,Omega[Xomega[rho]]) + Multiply(r_3_beta_2,Omega[Xomega[rho]]) + r_3_beta_2_flux + Multiply(r_cg_beta,Multiply(Omega[Xomega[2]],Multiply(R[beta[2]],R[psi[2]])));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVExUl9jZ19iZXRhXzJfZmx1eEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtYWN0aW9uR0YkNiUtSShtZmVuY2VkR0YkNigtSSdtdGFibGVHRiQ2NS1JJG10ckdGJDYoLUkkbXRkR0YkNigtRiM2KS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GXm8tRiM2Ki1GLDYlUSJlRidGL0YyLUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GaW8tRiM2KC1GLDYlUSRzaW5GJy9GMEY9RjktRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRmhvRmpvLUZTNiQtRiM2Ji1GLDYlUScmIzk2ODtGJ0ZgcEY5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9RjlGOUZbcUZecUY5RmVvLUklbXN1YkdGJDYlRmhwLUYjNiYtRiw2JVElZmx1eEYnRi9GMkZbcUZecUY5LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGW3FGXnFGOS1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIRl1vRl9vLUYjNigtSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JFEiMUYnRjktRmRyNiRRIjJGJ0Y5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zfcy8lKWJldmVsbGVkR0Y9RmVvLUYjNigtRiw2JVEiUkYnRi9GMkZlby1GUzYkLUYjNigtRiM2KC1GUzYkLUYjNilGam4tRiM2Ki1GYXE2JS1GLDYlUScmIzk2MTtGJ0ZgcEY5RmNxRmhxRmVvRltwRmVvLUYjNihGXXBGYXAtRlM2JC1GIzYmLUZhcTYlLUYsNiVRJyYjOTQ2O0YnRmBwRjktRiM2JkZnckZbcUZecUY5RmhxRltxRl5xRjlGOUZbcUZecUY5RltxRl5xRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSEZdb0Zfby1GIzYoLUYsNiVRJyYjOTM3O0YnRmBwRjlGZW8tRiM2KC1GLDYlUSRjb3NGJ0ZgcEY5RmFwRlx1RltxRl5xRjlGW3FGXnFGOUZbcUZecUY5RjlGZW9GW3BGW3FGXnFGOUZbci1GIzYqLUZTNiQtRiM2KUZqbi1GIzYoRmV0RmVvLUYjNihGYXZGYXBGZHBGW3FGXnFGOUZbcUZecUY5Rmd1LUZhcTYlRmJ1LUYjNiYtRmFxNiVGZXFGZXVGaHFGW3FGXnFGOUZocUZbcUZecUY5RjlGZW9GXHdGZW9GanRGW3FGXnFGOUZbcUZecUY5RjlGW3FGXnFGOUZbcUZecUY5RltxRl5xRjkvJSlyb3dhbGlnbkdRIUYnLyUsY29sdW1uYWxpZ25HRmZ3LyUrZ3JvdXBhbGlnbkdGZncvJShyb3dzcGFuR0Zccy8lK2NvbHVtbnNwYW5HRlxzLUZmbjYoLUYjNilGam4tRiM2KkZib0Zlb0Zcd0Zlb0ZgcUZbcUZecUY5RltyLUYjNihGYHJGZW8tRiM2KEZmc0Zlby1GUzYkLUYjNigtRiM2KEZfdEZlb0Zcd0ZbcUZecUY5Rmd1LUYjNipGZnZGZW9GW3BGZW9GanRGW3FGXnFGOUZbcUZecUY5RjlGW3FGXnFGOUZbcUZecUY5RltxRl5xRjlGZHdGZ3dGaXdGW3hGXXgtRmZuNigtRiM2K0Zqbi1GIzYoRmByRmVvLUYjNigtRiw2JVEibEYnRi9GMkZlb0ZldEZbcUZecUY5RltxRl5xRjlGZ3UtRiM2KkZib0Zlb0Zcd0Zlb0ZldEZbcUZecUY5RltyLUYjNihGYHJGZW8tRiM2KkZmc0Zlb0ZmdkZlb0ZfdkZbcUZecUY5RltxRl5xRjlGW3FGXnFGOUZkd0Znd0Zpd0ZbeEZdeEZkd0Znd0Zpdy8lJmFsaWduR1ElYXhpc0YnL0Zld1EpYmFzZWxpbmVGJy9GaHdGX3MvRmp3USd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGMS8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRl5bbC8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0ZpW2wvJSZmcmFtZUdGaVtsLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGPS8lLWVxdWFsY29sdW1uc0dGPS8lLWRpc3BsYXlzdHlsZUdGPS8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0ZmW2xGOS9JK21zZW1hbnRpY3NHRiRRKlJvd1ZlY3RvckYnLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRlxdbC8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRKjE1MTg5Nzc4NEYnRltxRl5xRjk=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L255" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_T_flux := Multiply(r_cg_T,Omega[Xomega[rho]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkksUl9jZ19UX2ZsdXhHNiItSSdSVEFCTEVHRiQ2JSIqX2VoayItSSdWRUNUT1JHRiQ2IzclIiIhRi0sJCooIyIiIiIiJUYxSSJsR0YkRjEmSSRyaG9HRiQ2I0klZmx1eEdGJEYxISIiJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHJvd0dGJA==">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</Equation></Text-field>
</Output>
</Group></Presentation-Block>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Inertia matrices of cg</Text-field></Title>
<Group labelreference="L144" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">JB = (1/12)*m_b*R*R;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">L0kjSkJHNiIsJCooIyIiIiIjN0YoSSRtX2JHRiRGKClJIlJHRiQiIiNGKEYo</Equation></Text-field>
</Output>
</Group><Presentation-Block>
<Group view="code" labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">J[blade] := Matrix([[0,0,0],[0,JB,0],[0,0,JB]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkpHNiI2I0kmYmxhZGVHRiUtSSdSVEFCTEVHRiU2JSIqS1FrayItSSdNQVRSSVhHRiU2IzclNyUiIiFGMUYxNyVGMUkjSkJHRiVGMTclRjFGMUYzSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU=">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L145" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">JT = (1/12)*m_t*(l/2)*(l/2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjSlRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiM2KC1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGOS1GVTYkUSM0OEYnRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmpuLyUpYmV2ZWxsZWRHRj0tRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZjby1GIzYoLUYsNiVRJG1fdEYnRi9GMkZfby1JJW1zdXBHRiQ2JS1GLDYlUSJsRidGL0YyLUZVNiRRIjJGJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5RmZwRmlwRjlGZnBGaXBGOQ==">L0kjSlRHNiIsJCooIyIiIiIjW0YoSSRtX3RHRiRGKClJImxHRiQiIiNGKEYo</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">J[tower] := Matrix([[0,0,0],[0,JT,0],[0,0,JT]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkpHNiI2I0kmdG93ZXJHRiUtSSdSVEFCTEVHRiU2JSIqV3ZYYCItSSdNQVRSSVhHRiU2IzclNyUiIiFGMUYxNyVGMUkjSlRHRiVGMTclRjFGMUYzSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU=">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</Equation></Text-field>
</Output>
</Group></Presentation-Block>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Kinetic energy: translational part</Text-field></Title>
<Group labelreference="L262" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T_blade_1 := 0.5*m_b*((R_cg_beta_1_flux[1]*R_cg_beta_1_flux[1])+(R_cg_beta_1_flux[2]*R_cg_beta_1_flux[2])+(R_cg_beta_1_flux[3]*R_cg_beta_1_flux[3]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L260" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T_blade_2 := 0.5*m_b*((R_cg_beta_2_flux[1]*R_cg_beta_2_flux[1])+(R_cg_beta_2_flux[2]*R_cg_beta_2_flux[2])+(R_cg_beta_2_flux[3]*R_cg_beta_2_flux[3]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L261" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T_tower := 0.5*m_t*((R_cg_T_flux[1]*R_cg_T_flux[1])+(R_cg_T_flux[2]*R_cg_T_flux[2])+(R_cg_T_flux[3]*R_cg_T_flux[3]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoVF90b3dlckc2IiwkKiokIisrKytESiEjNiIiIkkkbV90R0YkRiopSSJsR0YkIiIjRiopJkkkcmhvR0YkNiNJJWZsdXhHRiRGLkYqRio=">LCQqKiQiKysrK0RKISM2IiIiSSRtX3RHNiJGJylJImxHRikiIiNGJykmSSRyaG9HRik2I0klZmx1eEdGKUYsRidGJw==</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Kinetic energy: rotational part</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L556" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="code" labelreference="L239" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">D_blade_1 := Multiply(omega[1],J[blade]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkqRF9ibGFkZV8xRzYiLUknUlRBQkxFR0YkNiUiKl9paGsiLUknVkVDVE9SR0YkNiM3JSIiISomLCYqJiZJJHJob0dGJDYjSSVmbHV4R0YkIiIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHBzaUdGJEY1ISIiJkklYmV0YUdGJDYjJkY0NiNGNUY1RjVJI0pCR0YkRjUqJiwmKihGMUY1LUkkc2luR0Y4RjtGNS1GSDYjJkY/RkJGNUY1KiZJJk9tZWdhR0YkRjUtRjdGSkY1Rj1GNUZDRjUmSSdWZWN0b3JHRjg2I0kkcm93R0Yk">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L263" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">D_blade_2 := Multiply(omega[2],J[blade]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkqRF9ibGFkZV8yRzYiLUknUlRBQkxFR0YkNiUiKms4KTQ6LUknVkVDVE9SR0YkNiM3JSIiISomLCYqJiZJJHJob0dGJDYjSSVmbHV4R0YkIiIiLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHBzaUdGJEY1RjUmSSViZXRhR0YkNiMmRjQ2IyIiI0Y1RjVJI0pCR0YkRjUqJiwmKihGMUY1LUkkc2luR0Y4RjtGNS1GSDYjJkY+RkFGNSEiIiomSSZPbWVnYUdGJEY1LUY3RkpGNUZMRjVGQ0Y1JkknVmVjdG9yR0Y4NiNJJHJvd0dGJA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEqRF9ibGFkZV8yRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JKG1hY3Rpb25HRiQ2JS1JKG1mZW5jZWRHRiQ2KC1JJ210YWJsZUdGJDY1LUkkbXRyR0YkNigtSSRtdGRHRiQ2KC1JI21uR0YkNiRRIjBGJ0Y5LyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0Zeby8lK2dyb3VwYWxpZ25HRl5vLyUocm93c3BhbkdRIjFGJy8lK2NvbHVtbnNwYW5HRmVvLUZmbjYoLUYjNigtRlM2JC1GIzYoLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEnJiM5NjE7RicvRjBGPUY5LUYjNiYtRiw2JVElZmx1eEYnRi9GMi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZqcS1GIzYoLUYsNiVRJGNvc0YnRmhwRjktRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRmlxRltyLUZTNiQtRiM2Ji1GLDYlUScmIzk2ODtGJ0ZocEY5Rl5xRmFxRjlGOUZecUZhcUY5Rl5xRmFxRjktRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZfcy1GY3A2JS1GLDYlUScmIzk0NjtGJ0ZocEY5LUYjNiYtRmNwNiVGW3EtRiM2Ji1GaW42JFEiMkYnRjlGXnFGYXFGOUZjcUZecUZhcUY5RmNxRl5xRmFxRjlGOUZmcS1GLDYlUSNKQkYnRi9GMkZecUZhcUY5RlxvRl9vRmFvRmNvRmZvLUZmbjYoLUYjNigtRlM2JC1GIzYpLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSEZec0Zgcy1GIzYqRmJwRmZxLUYjNigtRiw2JVEkc2luRidGaHBGOUZhckZkckZecUZhcUY5RmZxLUYjNihGYXVGYXItRlM2JC1GIzYmLUZjcDYlRmNzRmpzRmNxRl5xRmFxRjlGOUZecUZhcUY5Rl5xRmFxRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSEZec0Zgcy1GIzYoLUYsNiVRJyYjOTM3O0YnRmhwRjlGZnEtRiM2KEZeckZhckZmdUZecUZhcUY5Rl5xRmFxRjlGXnFGYXFGOUY5RmZxRl90Rl5xRmFxRjlGXG9GX29GYW9GY29GZm9GXG9GX29GYW8vJSZhbGlnbkdRJWF4aXNGJy9GXW9RKWJhc2VsaW5lRicvRmBvUSdjZW50ZXJGJy9GYm9RJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0YxLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGY3cvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGXngvJSZmcmFtZUdGXngvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0Y9LyUtZXF1YWxjb2x1bW5zR0Y9LyUtZGlzcGxheXN0eWxlR0Y9LyUlc2lkZUdRJnJpZ2h0RicvJTBtaW5sYWJlbHNwYWNpbmdHRlt4RjkvSSttc2VtYW50aWNzR0YkUSpSb3dWZWN0b3JGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZheS8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRKjE1MDUyMDI1NkYnRl5xRmFxRjk=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L264" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">D_tower := Multiply(omega[rho],J[tower]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoRF90b3dlckc2Ii1JJ1JUQUJMRUdGJDYlIipDZjFeIi1JJ1ZFQ1RPUkdGJDYjNyUiIiEqJiZJJHJob0dGJDYjSSVmbHV4R0YkIiIiSSNKVEdGJEYzRi0mSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcm93R0Yk">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L265" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T_rot_blade_1 := 0.5*((D_blade_1[1]*omega[1][1])+(D_blade_1[2]*omega[1][2])+(D_blade_1[3]*omega[1][3]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkuVF9yb3RfYmxhZGVfMUc2IiwmKigkIiImISIiIiIiKSwmKiYmSSRyaG9HRiQ2I0klZmx1eEdGJEYqLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHBzaUdGJEYqRikmSSViZXRhR0YkNiMmRjE2I0YqRioiIiNGKkkjSkJHRiRGKkYqKihGJ0YqKSwmKihGLkYqLUkkc2luR0Y0RjdGKi1GRTYjJkY6Rj1GKkYqKiZJJk9tZWdhR0YkRiotRjNGR0YqRilGPkYqRj9GKkYq">LCYqKCQiIiYhIiIiIiIpLCYqJiZJJHJob0c2IjYjSSVmbHV4R0YtRictSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRi02I0kkcHNpR0YtRidGJiZJJWJldGFHRi02IyZGLzYjRidGJyIiI0YnSSNKQkdGLUYnRicqKEYkRicpLCYqKEYrRictSSRzaW5HRjJGNUYnLUZDNiMmRjhGO0YnRicqJkkmT21lZ2FHRi1GJy1GMUZFRidGJkY8RidGPUYnRic=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L266" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T_rot_blade_2 := 0.5*((D_blade_2[1]*omega[2][1])+(D_blade_2[2]*omega[2][2])+(D_blade_2[3]*omega[2][3]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkuVF9yb3RfYmxhZGVfMkc2IiwmKigkIiImISIiIiIiKSwmKiYmSSRyaG9HRiQ2I0klZmx1eEdGJEYqLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNJJHBzaUdGJEYqRiomSSViZXRhR0YkNiMmRjE2IyIiI0YqRj5GKkkjSkJHRiRGKkYqKihGJ0YqKSwmKihGLkYqLUkkc2luR0Y0RjdGKi1GRTYjJkY6Rj1GKkYpKiZJJk9tZWdhR0YkRiotRjNGR0YqRilGPkYqRj9GKkYq">LCYqKCQiIiYhIiIiIiIpLCYqJiZJJHJob0c2IjYjSSVmbHV4R0YtRictSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRi02I0kkcHNpR0YtRidGJyZJJWJldGFHRi02IyZGLzYjIiIjRidGPEYnSSNKQkdGLUYnRicqKEYkRicpLCYqKEYrRictSSRzaW5HRjJGNUYnLUZDNiMmRjhGO0YnRiYqJkkmT21lZ2FHRi1GJy1GMUZFRidGJkY8RidGPUYnRic=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L267" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T_rot_tower := 0.5*((D_tower[1]*omega[rho][1])+(D_tower[2]*omega[rho][2])+(D_tower[3]*omega[rho][3]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkksVF9yb3RfdG93ZXJHNiIsJCooJCIiJiEiIiIiIikmSSRyaG9HRiQ2I0klZmx1eEdGJCIiI0YqSSNKVEdGJEYqRio=">LCQqKCQiIiYhIiIiIiIpJkkkcmhvRzYiNiNJJWZsdXhHRisiIiNGJ0kjSlRHRitGJ0Yn</Equation></Text-field>
</Output>
</Group></Presentation-Block>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Total kinetic energy</Text-field></Title>
<Group labelreference="L269" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T_total := T_blade_1 + T_blade_2 + T_tower + T_rot_blade_1 + T_rot_blade_2 + T_rot_tower;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L425" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">`starting length` = length(%), `converting to horner`=length(convert(%,horner)), factoring=length(factor(%)), `simplify length` = length(symplify(%));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiYvSTBzdGFydGluZ35sZW5ndGhHNiIiJWc9L0k1Y29udmVydGluZ350b35ob3JuZXJHRiUiJXpVL0kqZmFjdG9yaW5nR0YlIiVFXS9JMHNpbXBsaWZ5fmxlbmd0aEdGJSIldD0=</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Potential energy</Text-field></Title>
<Group labelreference="L273" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">g := Vector[row]([g_,0,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiZ0c2Ii1JJ1JUQUJMRUdGJDYlIio/WF1rIi1JJ1ZFQ1RPUkdGJDYjNyVJI2dfR0YkIiIhRi4mSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kkcm93R0Yk">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</Equation></Text-field>
</Output>
</Group><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L277" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Position vectors expressed in {E_0} for the potential energy</Text-field>
</Input>
</Group></Presentation-Block>
<Group labelreference="L274" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_blade_1_0 := r_0 + Multiply(r_2,R[rho]) + Multiply(r_3_beta_1,R[rho]) + Multiply(r_cg_beta,Multiply(R[beta[1]],Multiply(R[psi[1]],R[rho])));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L275" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_blade_2_0 := r_0 + Multiply(r_2,R[rho]) + Multiply(r_3_beta_2,R[rho]) + Multiply(r_cg_beta,Multiply(R[beta[2]],Multiply(R[psi[2]],R[rho])));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L276" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">R_cg_T_0 := r_0 + Multiply(r_cg_T,R[rho]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkpUl9jZ19UXzBHNiItSSdSVEFCTEVHRiQ2JSIqN0cpXDstSSdWRUNUT1JHRiQ2IzclLCYqJiMiIiIiIiNGMEkibEdGJEYwRjAqKCNGMCIiJUYwRjJGMC1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSRyaG9HRiRGMEYwIiIhLCQqKEY0RjBGMkYwLUkkc2luR0Y4RjtGMCEiIiZJJ1ZlY3RvckdGODYjSSRyb3dHRiQ=">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</Equation></Text-field>
</Output>
</Group><Presentation-Block>
<Group view="code" labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">V_g := (m_b*g[1]*(R_cg_blade_1_0[1] + R_cg_blade_2_0[1]))+(m_t*g[1]*R_cg_T_0[1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkVl9nRzYiLCYqKEkkbV9iR0YkIiIiSSNnX0dGJEYoLCpJImxHRiRGKComRitGKC1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSRyaG9HRiRGKEYoKigjRigiIiNGKEkiUkdGJEYoLCYqKC1GLjYjJkklYmV0YUdGJDYjRihGKC1GLjYjSSRwc2lHRiRGKEYtRighIiIqJi1JJHNpbkdGL0Y7RigtRkVGMkYoRkJGKEYoKihGNUYoRjdGKCwmKigtRi42IyZGPTYjRjZGKEY/RihGLUYoRigqJi1GRUZLRihGRkYoRkJGKEYoRihGKCooSSRtX3RHRiRGKEYpRigsJiomRjVGKEYrRihGKCooI0YoIiIlRihGK0YoRi1GKEYoRihGKA==">LCYqKEkkbV9iRzYiIiIiSSNnX0dGJUYmLCpJImxHRiVGJiomRilGJi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRyaG9HRiVGJkYmKigjRiYiIiNGJkkiUkdGJUYmLCYqKC1GLDYjJkklYmV0YUdGJTYjRiZGJi1GLDYjSSRwc2lHRiVGJkYrRiYhIiIqJi1JJHNpbkdGLUY5RiYtRkNGMEYmRkBGJkYmKihGM0YmRjVGJiwmKigtRiw2IyZGOzYjRjRGJkY9RiZGK0YmRiYqJi1GQ0ZJRiZGREYmRkBGJkYmRiZGJiooSSRtX3RHRiVGJkYnRiYsJiomRjNGJkYpRiZGJiooI0YmIiIlRiZGKUYmRitGJkYmRiZGJg==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L72" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">V_springs := 1/2*kb*beta[1]*beta[1]+1/2*kb*beta[2]*beta[2]+1/2*ka*rho*rho;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkqVl9zcHJpbmdzRzYiLCgqKCMiIiIiIiNGKEkja2JHRiRGKCkmSSViZXRhR0YkNiNGKEYpRihGKCooRidGKEYqRigpJkYtNiNGKUYpRihGKCooRidGKEkja2FHRiRGKClJJHJob0dGJEYpRihGKA==">LCgqKCMiIiIiIiNGJUkja2JHNiJGJSkmSSViZXRhR0YoNiNGJUYmRiVGJSooRiRGJUYnRiUpJkYrNiNGJkYmRiVGJSooRiRGJUkja2FHRihGJSlJJHJob0dGKEYmRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L102" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">V_total := V_g + V_springs;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqKEkkbV9iRzYiIiIiSSNnX0dGJUYmLCpJImxHRiVGJiomRilGJi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSRyaG9HRiVGJkYmKigjRiYiIiNGJkkiUkdGJUYmLCYqKC1GLDYjJkklYmV0YUdGJTYjRiZGJi1GLDYjSSRwc2lHRiVGJkYrRiYhIiIqJi1JJHNpbkdGLUY5RiYtRkNGMEYmRkBGJkYmKihGM0YmRjVGJiwmKigtRiw2IyZGOzYjRjRGJkY9RiZGK0YmRiYqJi1GQ0ZJRiZGREYmRkBGJkYmRiZGJiooSSRtX3RHRiVGJkYnRiYsJiomRjNGJkYpRiZGJiooI0YmIiIlRiZGKUYmRitGJkYmRiZGJiooRjNGJkkja2JHRiVGJilGOkY0RiZGJiooRjNGJkZWRiYpRkpGNEYmRiYqKEYzRiZJI2thR0YlRiYpRjFGNEYmRiY=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L452" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">`starting length` = length(V_total), `converting to horner`=length(convert(V_total,horner)), factoring=length(factor(V_total)), `simplify length` = length(symplify(V_total));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiYvSTBzdGFydGluZ35sZW5ndGhHNiIiJCdRL0k1Y29udmVydGluZ350b35ob3JuZXJHRiUiJGYkL0kqZmFjdG9yaW5nR0YlIiRXJS9JMHNpbXBsaWZ5fmxlbmd0aEdGJSIkKlI=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L92" drawlabel="true">
</Group></Presentation-Block>
</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Full equations of motion using the Lagrangian</Text-field></Title>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">eq of motion for beta_1</Text-field></Title>
<Group labelreference="L302" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta1flux := diff(T_total, beta[flux[1]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L303" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta1 := diff(T_total, beta[1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L304" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dV_dbeta1 := diff(V_total, beta[1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkqZFZfZGJldGExRzYiLCYqLCMiIiIiIiNGKEkkbV9iR0YkRihJI2dfR0YkRihJIlJHRiRGKCwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyZJJWJldGFHRiQ2I0YoRigtSSRjb3NHRjE2I0kkcHNpR0YkRigtRjk2I0kkcmhvR0YkRihGKComLUY5RjRGKC1GMEY9RighIiJGKEYoKiZJI2tiR0YkRihGNUYoRig=">LCYqLCMiIiIiIiNGJUkkbV9iRzYiRiVJI2dfR0YoRiVJIlJHRihGJSwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRig2IyZJJWJldGFHRig2I0YlRiUtSSRjb3NHRi82I0kkcHNpR0YoRiUtRjc2I0kkcmhvR0YoRiVGJSomLUY3RjJGJS1GLkY7RiUhIiJGJUYlKiZJI2tiR0YoRiVGM0YlRiU=</Equation></Text-field>
</Output>
</Group>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">indicate time dependencies</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L318" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">indicate time dependencies</Text-field>
</Input>
</Group></Presentation-Block>
<Group labelreference="L308" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta1_t := subs({beta[flux[1]]=beta[flux[1]](t),beta[flux[2]]=beta[flux[2]](t),rho[flux]=rho[flux](t), psi[flux]=Omega, beta[1]=beta[1](t), beta[2]=beta[2](t), rho=rho(t), psi=Omega*t},dT_dbeta1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L311" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dV_dbeta1_t := subs({beta[flux[1]]=beta[flux[1]](t),beta[flux[2]]=beta[flux[2]](t),rho[flux]=rho[flux](t), psi[flux]=Omega, beta[1]=beta[1](t), beta[2]=beta[2](t), rho=rho(t), psi=Omega*t},dV_dbeta1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkksZFZfZGJldGExX3RHNiIsJiosIyIiIiIiI0YoSSRtX2JHRiRGKEkjZ19HRiRGKEkiUkdGJEYoLCYqKC1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLSZJJWJldGFHRiQ2I0YoNiNJInRHRiRGKC1JJGNvc0dGMTYjKiZJJk9tZWdhR0YkRihGOkYoRigtRjw2Iy1JJHJob0dGJEY5RihGKComLUY8RjRGKC1GMEZBRighIiJGKEYoKiZJI2tiR0YkRihGNUYoRig=">LCYqLCMiIiIiIiNGJUkkbV9iRzYiRiVJI2dfR0YoRiVJIlJHRihGJSwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRig2Iy0mSSViZXRhR0YoNiNGJTYjSSJ0R0YoRiUtSSRjb3NHRi82IyomSSZPbWVnYUdGKEYlRjhGJUYlLUY6NiMtSSRyaG9HRihGN0YlRiUqJi1GOkYyRiUtRi5GP0YlISIiRiVGJSomSSNrYkdGKEYlRjNGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L310" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta1flux_t := subs({beta[flux[1]]=beta[flux[1]](t),beta[flux[2]]=beta[flux[2]](t),rho[flux]=rho[flux](t), psi[flux]=Omega, beta[1]=beta[1](t), beta[2]=beta[2](t), rho=rho(t), psi=Omega*t},dT_dbeta1flux);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L317" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">change q_flux to d/dt(q)</Text-field>
</Input>
</Group></Presentation-Block>
<Group labelreference="L314" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta1_tt := subs({beta[flux[1]](t)=diff(beta[1](t),t),beta[flux[2]](t)=diff(beta[2](t),t),rho[flux](t)=diff(rho(t),t)},dT_dbeta1_t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L315" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dV_dbeta1_tt := subs({beta[flux[1]](t)=diff(beta[1](t),t),beta[flux[2]](t)=diff(beta[2](t),t),rho[flux](t)=diff(rho(t),t)},dV_dbeta1_t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkktZFZfZGJldGExX3R0RzYiLCYqLCMiIiIiIiNGKEkkbV9iR0YkRihJI2dfR0YkRihJIlJHRiRGKCwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2Iy0mSSViZXRhR0YkNiNGKDYjSSJ0R0YkRigtSSRjb3NHRjE2IyomSSZPbWVnYUdGJEYoRjpGKEYoLUY8NiMtSSRyaG9HRiRGOUYoRigqJi1GPEY0RigtRjBGQUYoISIiRihGKComSSNrYkdGJEYoRjVGKEYo">LCYqLCMiIiIiIiNGJUkkbV9iRzYiRiVJI2dfR0YoRiVJIlJHRihGJSwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRig2Iy0mSSViZXRhR0YoNiNGJTYjSSJ0R0YoRiUtSSRjb3NHRi82IyomSSZPbWVnYUdGKEYlRjhGJUYlLUY6NiMtSSRyaG9HRihGN0YlRiUqJi1GOkYyRiUtRi5GP0YlISIiRiVGJSomSSNrYkdGKEYlRjNGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L316" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta1flux_tt := subs({beta[flux[1]](t)=diff(beta[1](t),t),beta[flux[2]](t)=diff(beta[2](t),t),rho[flux](t)=diff(rho(t),t)},dT_dbeta1flux_t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L460" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">`starting length` = length(%), `converting to horner`=length(convert(%,horner)), factoring=length(factor(%)), `simplify length` = length(symplify(%));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiYvSTBzdGFydGluZ35sZW5ndGhHNiIiJSg9Ii9JNWNvbnZlcnRpbmd+dG9+aG9ybmVyR0YlIiRwKC9JKmZhY3RvcmluZ0dGJSIkViovSTBzaW1wbGlmeX5sZW5ndGhHRiUiJSs3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L561" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta1flux_tt := convert(dT_dbeta1flux_tt, horner);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">differentiate with respect to t and construct equations of motion for beta 1</Text-field></Title>
<Group labelreference="L332" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ddt_dT_dbeta1flux := diff(dT_dbeta1flux_tt, t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L448" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">`starting length` = length(%), `converting to horner`=length(convert(%,horner)), factoring=length(factor(%)), `simplify length` = length(symplify(%));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiYvSTBzdGFydGluZ35sZW5ndGhHNiIiJSZbIy9JNWNvbnZlcnRpbmd+dG9+aG9ybmVyR0YlIiVuQC9JKmZhY3RvcmluZ0dGJSIlSkYvSTBzaW1wbGlmeX5sZW5ndGhHRiUiJSlcIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L449" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ddt_dT_dbeta1flux := convert(ddt_dT_dbeta1flux, horner);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L333" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">eq_beta1[full] := ddt_dT_dbeta1flux - dT_dbeta1_tt + dV_dbeta1_tt = 0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L450" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">`starting length` = length(%), `converting to horner`=length(convert(%,horner)), factoring=length(factor(%)), `simplify length` = length(symplify(%));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiYvSTBzdGFydGluZ35sZW5ndGhHNiIiJWpVL0k1Y29udmVydGluZ350b35ob3JuZXJHRiUiJXJKL0kqZmFjdG9yaW5nR0YlIiVSUy9JMHNpbXBsaWZ5fmxlbmd0aEdGJSIld1U=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L451" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">eq_beta1[full]:= convert(eq_beta1[full], horner);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L567" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">eq_beta1[full] := solve(eq_beta1[full],diff(beta[1](t),t,t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">simplify expression and lose time dependencie notation and d/dt</Text-field></Title>
<Group labelreference="L481" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T1_eq_beta1[full]:= subs({diff(beta[1](t),t,t)=bb_FF_1,diff(beta[2](t),t,t)=bb_FF_2,diff(rho(t),t,t)=aa_FF},eq_beta1[full]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJLFQxX2VxX2JldGExRzYiNiNJJWZ1bGxHRiUsJCooJCIiIiIiIUYrLF5vKiokIiIlRixGK0kjSkJHRiVGK0kmYWFfRkZHRiVGKy1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiZJJk9tZWdhR0YlRitJInRHRiVGK0YrISIiKi5GL0YrRjFGKyktRjQ2Iy0mSSViZXRhR0YlNiNGKzYjRjsiIiNGKy1JJWRpZmZHRjY2JC1JJHJob0dGJUZFRjtGKy1JJHNpbkdGNUY4RitGOkYrRisqLEYvRitGMUYrRkdGK0ZMRitGOkYrRisqLkYqRitJJG1fYkdGJUYrKUkiUkdGJUZGRitGPkYrRjJGK0YzRitGPCosRlJGK0ZQRitJImxHRiVGK0YyRitGP0YrRisqLkYqRitGUEYrRlFGKylGMyIiJEYrKS1GTUZARkZGK0YyRitGPCowJEZGRixGK0ZQRitGMkYrRjNGK0ZSRitGP0YrSSJlR0YlRitGPCowRipGK0ZQRitGUUYrRlhGKylGTEZGRitGMkYrRjNGK0Y8KihGL0YrSSNrYkdGJUYrRkFGK0YrKjJGZW5GK0ZQRitGR0YrRkxGK0Y6RitGUkYrRj9GK0ZmbkYrRisqLkZQRitGUUYrKUYzRkZGK0ZZRitGP0YrKS1GSDYkRkFGO0ZGRitGKyouRlBGK0ZRRitGPkYrRkdGK0ZMRitGOkYrRisqLkYqRitGUEYrRlFGK0Y/RitGWUYrRl5vRitGPCouRlBGK0ZRRitGWUYrRmhuRitGP0YrRl5vRitGKyosRi9GK0YxRispRjpGRkYrRj9GK0ZZRitGKyowRipGK0ZQRitGUUYrKUYzRjBGK0ZZRispRkdGRkYrRj9GK0Y8Ki5GL0YrRmhvRitGaG5GK0ZZRitGMUYrRj9GK0Y8KjBGKkYrRlBGK0ZRRitGaG9GKylGTEYwRitGWUYrRj9GK0Y8KjJGZW5GK0ZQRitGUUYrRmhvRitGaG5GK0ZZRitGP0YrRl1vRitGPCouRlBGK0ZRRispRkxGV0YrRjpGK0Y+RitGR0YrRisqLkZQRitGUUYrRmhuRitGZW9GK0Y/RitGWUYrRisqMEZQRitGUUYrRkxGK0Y6RitGPkYrRl1vRitGR0YrRisqMkZlbkYrRlBGK0ZSRitGZm5GK0ZecEYrRjpGK0ZHRitGP0YrRisqMEZlbkYrRlBGK0ZSRitGZm5GK0ZobkYrRmVvRitGWUYrRisqNEZlbkYrRlBGK0ZSRitGZm5GK0ZMRitGOkYrRj9GK0Zdb0YrRkdGK0YrKi5GUEYrRlFGK0Zdb0YrRmVvRitGP0YrRllGK0YrKjBGZW5GK0ZQRitGUkYrRmZuRitGXW9GK0Zlb0YrRllGK0YrKjBGKkYrRlBGK0ZSRitGWUYrRlRGK0Zob0YrRjNGK0Y8KjBGZW5GK0ZQRitGUkYrRllGK0ZmbkYrRl1vRitGaG9GK0YrKi5GUEYrRlFGK0ZZRitGaG9GK0Zdb0YrRj9GK0YrKi5GL0YrRjFGK0ZHRitGTEYrRlhGK0Y6RitGPCowRmVuRitGUEYrSSNnX0dGJUYrRlJGK0ZZRitGM0YrLUY0NiNGSkYrRisqLkZlbkYrRlBGK0ZbcUYrRlJGK0Y/RistRk1GXXFGK0Y8RissKiomRi9GK0YxRitGKyoqRlFGK0ZQRitGaG5GK0ZYRitGKyooRlFGK0ZQRitGPkYrRisqKkZRRitGUEYrRl1vRitGWEYrRitGPEY8">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</Equation></Text-field>
</Output>
</Group><Presentation-Block>
<Group view="code" labelreference="L483" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T2_eq_beta1[full]:= subs({diff(beta[1](t),t)=bb_F_1,diff(beta[2](t),t)=bb_F_2, diff(rho(t),t)=aa_F},T1_eq_beta1[full]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCQiIiIiIiFGJSxebyoqJCIiJUYmRiVJI0pCRzYiRiVJJmFhX0ZGR0YsRiUtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiw2IyomSSZPbWVnYUdGLEYlSSJ0R0YsRiVGJSEiIiouSSRtX2JHRixGJSlJIlJHRiwiIiNGJSktRi82Iy0mSSViZXRhR0YsNiNGJTYjRjZGPEYlSSVhYV9GR0YsRiUtSSRzaW5HRjBGM0YlRjVGJUYlKi5GJEYlRjlGJUY6RiVGPkYlLUZHRj9GJSlJJ2JiX0ZfMUdGLEY8RiVGNyouRilGJSlGRUY8RiUpRkZGPEYlRklGJUYrRiVGPkYlRjcqMEYkRiVGOUYlRjpGJUZNRiUpRkZGKkYlRklGJUY+RiVGNyouRjlGJUY6RiVGSUYlRk5GJUY+RiVGSkYlRiUqMEYkRiVGOUYlRjpGJSlGLkYqRiVGSUYlRk1GJUY+RiVGNyowRjlGJUY6RiVGRkYlRjVGJUY9RiUpRi5GPEYlRkVGJUYlKjIkRjxGJkYlRjlGJUY6RiVGTUYlRk5GJUZJRiVGPkYlRlVGJUY3Ki5GOUYlRjpGJSlGRiIiJEYlRjVGJUY9RiVGRUYlRiUqMkZXRiVGOUYlRjtGJUkiZUdGLEYlRllGJUY1RiVGRUYlRj5GJUYlKi5GJEYlRjlGJUY6RiVGPUYlRi1GJUYuRiVGNyosRilGJUYrRiVGRUYlRkZGJUY1RiVGJSosRjtGJUY5RiVJImxHRixGJUYtRiVGPkYlRiUqLkYkRiVGOUYlRjpGJSlGLkZaRiUpRklGPEYlRi1GJUY3KjBGV0YlRjlGJUYtRiVGLkYlRjtGJUY+RiVGZm5GJUY3KjRGV0YlRjlGJUY7RiVGZm5GJUZGRiVGNUYlRj5GJUZVRiVGRUYlRiUqMEYkRiVGOUYlRjtGJUZJRiVGam5GJUZNRiVGLkYlRjcqMEZXRiVGOUYlRjtGJUZJRiVGZm5GJUZVRiVGTUYlRiUqLkY5RiVGOkYlRklGJUZNRiVGVUYlRj5GJUYlKi5GKUYlRitGJUZFRiVGRkYlRl1vRiVGNUYlRjcqMEYkRiVGOUYlRjpGJUZdb0YlRk5GJUYtRiVGLkYlRjcqKEYpRiVJI2tiR0YsRiVGQEYlRiUqLkYpRiVGK0YlRj1GJUZFRiVGRkYlRjVGJUYlKixGKUYlRitGJSlGNUY8RiVGPkYlRklGJUYlKi5GOUYlRjpGJUZORiVGaW9GJUY+RiVGSUYlRiUqMEZXRiVGOUYlRjtGJUZmbkYlRk5GJUZpb0YlRklGJUYlKi5GOUYlRjpGJUZVRiVGaW9GJUY+RiVGSUYlRiUqMEZXRiVGOUYlRjtGJUZmbkYlRlVGJUZpb0YlRklGJUYlKjBGV0YlRjlGJUkjZ19HRixGJUY7RiVGSUYlRi5GJS1GLzYjLUkkcmhvR0YsRkRGJUYlKi5GV0YlRjlGJUZfcEYlRjtGJUY+RiUtRkdGYXBGJUY3KjJGV0YlRjlGJUZFRiVGRkYlRjVGJUY7RiVGPkYlRmZuRiVGJSouRjlGJUY6RiVGVUYlRklGJUY+RiVGSkYlRiVGJSwqKiZGKUYlRitGJUYlKipGOkYlRjlGJUZORiVGXW9GJUYlKihGOkYlRjlGJUY9RiVGJSoqRjpGJUY5RiVGVUYlRl1vRiVGJUY3Rjc=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L482" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">T3_eq_beta1[full] := subs({beta[1](t)=bb_1, beta[2](t)=bb_2, rho(t)=aa, Omega=om},T2_eq_beta1[full]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L572" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">bb_FF_1 := T3_eq_beta1[full];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group></Presentation-Block>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3"></Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L586" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L570" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">eq of motion for beta_2</Text-field></Title>
<Group labelreference="L347" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta2flux := diff(T_total, beta[flux[2]]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L343" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta2 := diff(T_total, beta[2]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L348" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dV_dbeta2 := diff(V_total, beta[2]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkqZFZfZGJldGEyRzYiLCYqLCMiIiIiIiNGKEkkbV9iR0YkRihJI2dfR0YkRihJIlJHRiRGKCwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyZJJWJldGFHRiQ2I0YpRigtSSRjb3NHRjE2I0kkcHNpR0YkRigtRjk2I0kkcmhvR0YkRighIiIqJi1GOUY0RigtRjBGPUYoRj9GKEYoKiZJI2tiR0YkRihGNUYoRig=">LCYqLCMiIiIiIiNGJUkkbV9iRzYiRiVJI2dfR0YoRiVJIlJHRihGJSwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRig2IyZJJWJldGFHRig2I0YmRiUtSSRjb3NHRi82I0kkcHNpR0YoRiUtRjc2I0kkcmhvR0YoRiUhIiIqJi1GN0YyRiUtRi5GO0YlRj1GJUYlKiZJI2tiR0YoRiVGM0YlRiU=</Equation></Text-field>
</Output>
</Group>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">indicate time dependencies</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L340" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">indicate time dependencies</Text-field>
</Input>
</Group></Presentation-Block>
<Group labelreference="L354" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta2_t := subs({beta[flux[1]]=beta[flux[1]](t),beta[flux[2]]=beta[flux[2]](t),rho[flux]=rho[flux](t), psi[flux]=Omega, beta[1]=beta[1](t), beta[2]=beta[2](t), rho=rho(t), psi=Omega*t},dT_dbeta2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L355" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dV_dbeta2_t := subs({beta[flux[1]]=beta[flux[1]](t),beta[flux[2]]=beta[flux[2]](t),rho[flux]=rho[flux](t), psi[flux]=Omega, beta[1]=beta[1](t), beta[2]=beta[2](t), rho=rho(t), psi=Omega*t},dV_dbeta2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkksZFZfZGJldGEyX3RHNiIsJiosIyIiIiIiI0YoSSRtX2JHRiRGKEkjZ19HRiRGKEkiUkdGJEYoLCYqKC1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLSZJJWJldGFHRiQ2I0YpNiNJInRHRiRGKC1JJGNvc0dGMTYjKiZJJk9tZWdhR0YkRihGOkYoRigtRjw2Iy1JJHJob0dGJEY5RighIiIqJi1GPEY0RigtRjBGQUYoRkRGKEYoKiZJI2tiR0YkRihGNUYoRig=">LCYqLCMiIiIiIiNGJUkkbV9iRzYiRiVJI2dfR0YoRiVJIlJHRihGJSwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRig2Iy0mSSViZXRhR0YoNiNGJjYjSSJ0R0YoRiUtSSRjb3NHRi82IyomSSZPbWVnYUdGKEYlRjhGJUYlLUY6NiMtSSRyaG9HRihGN0YlISIiKiYtRjpGMkYlLUYuRj9GJUZCRiVGJSomSSNrYkdGKEYlRjNGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L358" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta2flux_t := subs({beta[flux[1]]=beta[flux[1]](t),beta[flux[2]]=beta[flux[2]](t),rho[flux]=rho[flux](t), psi[flux]=Omega, beta[1]=beta[1](t), beta[2]=beta[2](t), rho=rho(t), psi=Omega*t},dT_dbeta2flux);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L353" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">change q_flux to d/dt(q)</Text-field>
</Input>
</Group></Presentation-Block>
<Group labelreference="L359" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta2_tt := subs({beta[flux[1]](t)=diff(beta[1](t),t),beta[flux[2]](t)=diff(beta[2](t),t),rho[flux](t)=diff(rho(t),t)},dT_dbeta2_t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L356" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dV_dbeta2_tt := subs({beta[flux[1]](t)=diff(beta[1](t),t),beta[flux[2]](t)=diff(beta[2](t),t),rho[flux](t)=diff(rho(t),t)},dV_dbeta2_t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkktZFZfZGJldGEyX3R0RzYiLCYqLCMiIiIiIiNGKEkkbV9iR0YkRihJI2dfR0YkRihJIlJHRiRGKCwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2Iy0mSSViZXRhR0YkNiNGKTYjSSJ0R0YkRigtSSRjb3NHRjE2IyomSSZPbWVnYUdGJEYoRjpGKEYoLUY8NiMtSSRyaG9HRiRGOUYoISIiKiYtRjxGNEYoLUYwRkFGKEZERihGKComSSNrYkdGJEYoRjVGKEYo">LCYqLCMiIiIiIiNGJUkkbV9iRzYiRiVJI2dfR0YoRiVJIlJHRihGJSwmKigtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRig2Iy0mSSViZXRhR0YoNiNGJjYjSSJ0R0YoRiUtSSRjb3NHRi82IyomSSZPbWVnYUdGKEYlRjhGJUYlLUY6NiMtSSRyaG9HRihGN0YlISIiKiYtRjpGMkYlLUYuRj9GJUZCRiVGJSomSSNrYkdGKEYlRjNGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L357" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta2flux_tt := subs({beta[flux[1]](t)=diff(beta[1](t),t),beta[flux[2]](t)=diff(beta[2](t),t),rho[flux](t)=diff(rho(t),t)},dT_dbeta2flux_t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L461" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">`starting length` = length(%), `converting to horner`=length(convert(%,horner)), factoring=length(factor(%)), `simplify length` = length(symplify(%));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiYvSTBzdGFydGluZ35sZW5ndGhHNiIiJSg9Ii9JNWNvbnZlcnRpbmd+dG9+aG9ybmVyR0YlIiRQKS9JKmZhY3RvcmluZ0dGJSIkViovSTBzaW1wbGlmeX5sZW5ndGhHRiUiJSs3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L562" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">dT_dbeta2flux_tt := convert(dT_dbeta2flux_tt, horner);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">differentiate with respect to t and construct equations of motion for beta 2</Text-field></Title>
<Group labelreference="L352" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ddt_dT_dbeta2flux := diff(dT_dbeta2flux_tt, t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L462" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">`starting length` = length(%), `converting to horner`=length(convert(%,horner)), factoring=length(factor(%)), `simplify length` = length(symplify(%));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiYvSTBzdGFydGluZ35sZW5ndGhHNiIiJSxGL0k1Y29udmVydGluZ350b35ob3JuZXJHRiUiJSlSIy9JKmZhY3RvcmluZ0dGJSIlSkYvSTBzaW1wbGlmeX5sZW5ndGhHRiUiJTlG</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L463" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">ddt_dT_dbeta2flux := convert(ddt_dT_dbeta2flux,horner);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L339" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">eq_beta2[full] := ddt_dT_dbeta2flux - dT_dbeta2_tt + dV_dbeta2_tt = 0;</Text-field>
</Input>