project_02.jl

### A Pluto.jl notebook ###
# v0.20.23

#> [frontmatter]
#> title = "project 2_rev3_written_in"

using Markdown
using InteractiveUtils

# ╔═╡ 91f15f2c-7b4e-4f5f-8d45-9ebef77ce7dc
using LinearAlgebra, Plots

# ╔═╡ f17103ea-06bf-11f1-a2b0-79e68ed152eb
md"""# Project_02 - Multibody kinematic modeling

![Dual slider kinematics project](https://raw.githubusercontent.com/cooperrc/me5180-project_02/refs/heads/main/dual-slider.svg)

In this project, a rigid bar is connected to two sliding pistons along
the diagonal tracks. As the pistons move along the tracks, the rigid bar rotates at a constant rate, $\dot{\theta}_3 = 2~rad/s$. The figure above has three _relative_ ccoordinate systems that move with the bodies:

1. $x_1-y_1-$ describes piston 1 position and orientation, $\theta_1$
2. $x_2-y_2-$ describes piston 2 position and orientation, $\theta_2$
3. $x_3-y_3-$ describes the rigid bar position and orientation, $\theta_3$

Each of the pistons are on tracks at $\pm 45^o$ and the rotating rigid
bar is 10 cm. The hinges are mounted to the center of the pistons
connecting the ends of the rigid bar. 
 
In this project, you need to 

1. determine constraint equations $C(\mathbf{q},~t)$
2. solve for the velocities, $\dot{q}$ and accelerations, $\ddot{q}$
3. visualize the motion of the system as the rigid bar goes through at least one full rotation
"""

# ╔═╡ b79f52a8-8c00-4b70-9fc5-164b7735e70d
md"""# 1. Determine the Constraint equations C(q,t)


The system consists of two pistons constrained to slide along fixed diagonal tracks and connected by a rigid bar of fixed length L=0.10m
The pistons are connected to the ends of the rigid bar through ideal pin joints located at the piston centers.

The rigid bar rotates with a prescribed constant angular velocity $\theta_3$.

A global inertial coordinate system $(x, y)$ is defined with its origin at the intersection point of the two tracks. Each piston moves along a straight line defined by its track angles $\alpha_1$ and $\alpha_2$, respectively

**Generalized Coordinates:**

Instead of modeling each body with full rigid‑body coordinates, we use reduced generalized coordinates ->

$q=\begin{bmatrix}
s_1 \\
s_2 \\
\theta_3
\end{bmatrix}$

**Geometry:** 

The geometry of $r_1$ and $r_2$ are expressed below

$\mathbf{r}_{1} = s_1\begin{bmatrix}
cos{\theta}_{1} \\
sin{\theta}_{1}
\end{bmatrix}=s_1\begin{bmatrix}
cos(45) \\
sin(45)
\end{bmatrix}$
$\mathbf{r}_{2} = s_2\begin{bmatrix}
cos{\theta}_{2} \\
sin{\theta}_{2}
\end{bmatrix}=s_2\begin{bmatrix}
cos(135) \\
sin(135)
\end{bmatrix}$


**Setting up the Constraint Equation:**

The global position vectors of the pistons are written directly from the track geometry. The rigid bar enforces a distance constraint between the pistons. 

$(\mathbf{r}_{2}-\mathbf{r}_{1})^2=L^2$
$C(q,t)=(\mathbf{r}_{2}-\mathbf{r}_{1})*(\mathbf{r}_{2}-\mathbf{r}_{1})-L^2=0$

$\mathbf{r}_{2}-\mathbf{r}_{1}=\begin{bmatrix}
s_2cos(135)-s_1cos(45) \\
s_2sin(135)-s_1sin(45)
\end{bmatrix}=\begin{bmatrix}
s_2(-\frac{\sqrt{2}}{2})-s_1(\frac{\sqrt{2}}{2}) \\
s_2(\frac{\sqrt{2}}{2})-s_1(\frac{\sqrt{2}}{2})
\end{bmatrix}$


**Final Constraint Equation:**

Substituting the piston position expression gives

$C(q,t)=s_1^2+s_2^2-L^2=0$


**For Julia/Pluto Purposes:**

$C(q,t)=A^2-b^2=0$
$A=\mathbf{r}_{2}-\mathbf{r}_{1}=\begin{bmatrix}
s_2cos(135)-s_1cos(45) \\
s_2sin(135)-s_1sin(45)
\end{bmatrix}$
$b=L=\begin{bmatrix}
Lcos{\theta}_{3} \\
Lsin{\theta}_{3}
\end{bmatrix}$
"""


# ╔═╡ 279da94d-6a6a-4884-bc51-09a7c90edafe
md"""

**Vector from Piston 1 to Piston 2:**


${\theta}_{3}(t)=0$

$\mathbf{r}_{21} = \begin{bmatrix}
Lcos{\theta}_{3} \\
Lsin{\theta}_{3}
\end{bmatrix}$

$\mathbf{r}_{2} = \mathbf{r}_{1}+\mathbf{r}_{21}$

This vector is constrained to remain aligned with the rigid bar and have magnitude L.

**XY Directions:**

The constraint is enforced independently in the x- and y-directions, producing two scaler equations->

$s_2\begin{bmatrix}
cos(135) \\
sin(135)
\end{bmatrix}=s_1\begin{bmatrix}
cos(45) \\
sin(45)
\end{bmatrix} + \begin{bmatrix}
Lcos{\theta}_{3} \\
Lsin{\theta}_{3}
\end{bmatrix}$


$s_2\frac{-2}{\sqrt{2}}=s_1\frac{2}{\sqrt{2}}+Lcos{\theta}_{3}$
$s_2\frac{2}{\sqrt{2}}=s_1\frac{2}{\sqrt{2}}+Lsin{\theta}_{3}$


**Addition Method then isolate s value:**

Solving the coupled linear equations yields the pistion displacements->

s_1:

$0=\frac{4}{\sqrt{2}}s_1+L(cos{\theta}_{3}+sin{\theta}_{3})$
$0=2\sqrt{2}s_1+L(cos{\theta}_{3}+sin{\theta}_{3})$
$s_1=-\frac{L}{2\sqrt{2}}(cos{\theta}_{3}+sin{\theta}_{3})$


s_2:

$\frac{4}{\sqrt{2}}s_2=L(sin{\theta}_{3}-cos{\theta}_{3})$
$2{\sqrt{2}}s_2=L(sin{\theta}_{3}-cos{\theta}_{3})$
$s_2=\frac{L}{2\sqrt{2}}(sin{\theta}_{3}-cos{\theta}_{3})$

""" 

# ╔═╡ a31c2198-98d0-4e79-ba9b-74487a3fd967
md"""# 2. Solve for Velocities $\dot{q}$ and accelerations $\ddot{q}$

**Velocity:**

Differentiating the constraint equation with respect to time gives ->

$C(\dot{q},t)=2{s}_{1}\dot{s_1}+2{s}_{2}\dot{s_2}=0$
$C(\dot{q},t)={s}_{1}\dot{s_1}+{s}_{2}\dot{s_2}=0$
$C(\dot{q},t)=(-\frac{L}{2\sqrt{2}}(cos{\theta}_{3}+sin{\theta}_{3}))\dot{s_1}+(\frac{L}{2\sqrt{2}}(sin{\theta}_{3}-cos{\theta}_{3}))\dot{s_2}=0$


s_1:

$\dot{s_1}=\frac{L}{\sqrt{2}}(sin{\theta}_{3}-cos{\theta}_{3})$

s_2:

$\dot{s_2}=\frac{L}{\sqrt{2}}(cos{\theta}_{3}+sin{\theta}_{3})$

"""


# ╔═╡ 891f182c-18f8-401d-a984-b1b3de2e67b0
md"""

**Acceleration:**

Differentitating once more ->

$C(\ddot{q},t)=\dot{s_1}^2+s_1\ddot{s_1}+\dot{s_2}^2+s_2\ddot{s_2}=0$
$C(\ddot{q},t)=\dot{s_1}^2+\dot{s_2}^2+s_1\ddot{s_1}+s_2\ddot{s_2}=0$

$C(\ddot{q},t)=(\frac{L}{\sqrt{2}}(sin{\theta}_{3}-cos{\theta}_{3}))^2+(\frac{L}{\sqrt{2}}(cos{\theta}_{3}+sin{\theta}_{3}))^2+(-\frac{L}{2\sqrt{2}}(cos{\theta}_{3}+sin{\theta}_{3}))\ddot{s_1}+(\frac{L}{2\sqrt{2}}(sin{\theta}_{3}-cos{\theta}_{3}))\ddot{s_2}=0$

s_1:

$\ddot{s_1}=\frac{2L}{\sqrt{2}}(cos{\theta}_{3}+sin{\theta}_{3})$

s_2:

$\ddot{s_2}=\frac{2L}{\sqrt{2}}(-sin{\theta}_{3}+cos{\theta}_{3})$

"""


# ╔═╡ ea9a70e5-5790-4c11-97ae-690e6d9eb516
# -------------------------
# Parameters
# -------------------------
begin
	L = 0.10                  # bar length in meters (10 cm)
	ω3 = 2.0                  # rad/s
	θ30 = 0.0               # initial angle
	# Verify these track angles from your original assignment
	α1 = π/4                  # example: 45 deg
	α2 = 3*π/4                  # example: 45 deg (shift in angle accounted for later)
end

# ╔═╡ fbe15d42-7162-4218-88e1-018ed677b3f0
# Time
tspan = range(0, 4π/ω3, length=300)   # one full rotation

# ╔═╡ bcb494f9-a3df-46a7-9348-e2eac204e190
md"""
${\theta}_{3}(t)={\theta}_{3}+{\omega}_{3}t$
"""


# ╔═╡ b8e47bce-4ec8-4bf1-b64b-817e597a65b2
# -------------------------
# Functions
# -------------------------
θ3(t) = θ30 + ω3*t

# ╔═╡ 2cddd741-e951-432e-9c5c-8853488d3c6d
md"""
Position Inputs (Assumes ${\alpha}_{1}$ & ${\alpha_2}$ are equivalent):

$A=\begin{bmatrix}
~-cos({\alpha}_{1})~~~cos({\alpha}_{2}) \\
~-sin({\alpha}_{1})~~sin({\alpha}_{2})
\end{bmatrix}$


$b=\begin{bmatrix}
Lcos({\theta_3}) \\
Lsin({\theta_3})
\end{bmatrix}$

$s=A,~b$
"""

# ╔═╡ 588c45c6-4633-4e7f-9534-57709602170f
function solve_positions(t, α1, α2, L)
    θ = θ3(t)

    A = [
        -cos(α1)   cos(α2)
        -sin(α1)   sin(α2)
    ]

    b = [
        L*cos(θ)
        L*sin(θ)
    ]

    s = A \ b
    return s[1], s[2]
end

# ╔═╡ f09f7a94-7d0c-4485-ba10-be8f65eb456d
md"""
Velocity Inputs:

$A=\begin{bmatrix}
~-cos({\alpha}_{1})~~~cos({\alpha}_{2}) \\
~-sin({\alpha}_{1})~~sin({\alpha}_{2})
\end{bmatrix}$


$b=\begin{bmatrix}
-L{\omega}_{3}^2sin({\theta_3}) \\
L{\omega}_{3}^2cos({\theta_3})
\end{bmatrix}$

$\dot{s}=A,~b$
"""


# ╔═╡ f3004cb6-61b9-4eda-9472-8b313377577d
function solve_velocities(t, α1, α2, L, ω3)
    θ = θ3(t)

    A = [
        -cos(α1)   cos(α2)
        -sin(α1)   sin(α2)
    ]

    b = [
        -L*ω3*sin(θ)
         L*ω3*cos(θ)
    ]

    sdot = A \ b
    return sdot[1], sdot[2]
end

# ╔═╡ b3151f63-6c9f-4bf9-ae4c-9fa89d6bc1c0
md"""
Acceleration Inputs:

$A=\begin{bmatrix}
~-cos({\alpha}_{1})~~~cos({\alpha}_{2}) \\
~-sin({\alpha}_{1})~~sin({\alpha}_{2})
\end{bmatrix}$


$b=\begin{bmatrix}
-L{\omega}_{3}^2cos({\theta_3}) \\
-L{\omega}_{3}^2sin({\theta_3})
\end{bmatrix}$

$\ddot{s}=A,~b$

"""


# ╔═╡ a9ad74bb-1d7a-486c-a65c-295aaad37750
function solve_accelerations(t, α1, α2, L, ω3)
    θ = θ3(t)

    A = [
        -cos(α1)   cos(α2)
        -sin(α1)   sin(α2)
    ]

    b = [
        -L*ω3^2*cos(θ)
        -L*ω3^2*sin(θ)
    ]

    sddot = A \ b
    return sddot[1], sddot[2]
end

# ╔═╡ 735b0c96-cdb9-450e-a89d-1c76f2b15560
begin
    #Conditioning / singularity check for the 2×2 solve A*s = b
    # A depends only on the track angles α1 and α2 (constants in this project).
    A = [
        -cos(α1)   cos(α2)
        -sin(α1)   sin(α2)
    ]

    condA = cond(A)

    # Thresholds (rule of thumb)
    cond_warn = 100.0
    cond_bad  = 1000.0

    md"Conditioning check: cond(A) = $(round(condA, digits=3))  (warn > $(cond_warn), bad > $(cond_bad))"
end

# ╔═╡ 6c4c1d6c-05c9-4eba-ad6b-57d74b94f1c3
begin
    # Plot cond(A) as a constant line across the simulation time span
    condA_vals = fill(condA, length(tspan))

    p = plot(
        tspan, condA_vals,
        xlabel="Time (s)",
        ylabel="cond(A)",
        title="Condition Number of Solve Matrix A",
        legend=false,
        lw=2
    )

    hline!(p, [cond_warn], linestyle=:dash, lw=2)
    hline!(p, [cond_bad], linestyle=:dashdot, lw=2)

    p
end

# ╔═╡ 1f6e208c-e8bd-4974-9973-51b7d1a571f3
md"""
### Conditioning check

The 2×2 solve (A*s = b) is well-conditioned with cond(A) = 1.0, so the kinematics are far from singular and numerically stable.
"""


# ╔═╡ b1bd29d2-aabe-490d-8e58-1854f2de485f
# -------------------------
# Compute results
# -------------------------
s1_vals = Float64[]

# ╔═╡ 0a8aec35-ae14-491c-9926-becdad7bbf46
s2_vals = Float64[]

# ╔═╡ f4f50ebf-b7cc-4d13-be8f-90ea731502d5
s1dot_vals = Float64[]

# ╔═╡ bcb7995f-2061-495b-8f1f-b134d5222c04
s2dot_vals = Float64[]

# ╔═╡ 66646852-6945-4a81-98aa-9ca3cd5b54dd
s1ddot_vals = Float64[]

# ╔═╡ d25d2756-1f09-46f4-80b3-96389c4eca6c
s2ddot_vals = Float64[]

# ╔═╡ 1d0dcfeb-c2cc-4d09-88db-d6e9e430d7cc
md"""# 3. Visualize the Motion of the System as a Rigid Bar Goes through at least one Full Rotation
"""

# ╔═╡ a6889fc8-bbac-473a-9abf-1276db8eb901
for t in tspan
    s1, s2 = solve_positions(t, α1, α2, L)
    s1dot, s2dot = solve_velocities(t, α1, α2, L, ω3)
    s1ddot, s2ddot = solve_accelerations(t, α1, α2, L, ω3)

    push!(s1_vals, s1)
    push!(s2_vals, s2)
    push!(s1dot_vals, s1dot)
    push!(s2dot_vals, s2dot)
    push!(s1ddot_vals, s1ddot)
    push!(s2ddot_vals, s2ddot)
end

# ╔═╡ 2c48c51f-97ba-4c5c-aeed-afd29f735e65
md"""
	## Piston Kinematics As A Function of S1 and S2
	"""

# ╔═╡ 753ef8f1-c7e6-4728-ba19-69b852f108bb
plot(
    tspan,
    [s1_vals s2_vals],
    xlabel = "Time (s)",
    ylabel = "Position along track (m)",
    label = ["Piston 1" "Piston 2"],
    linewidth = 2,
    title = "Piston Positions vs Time"
)

# ╔═╡ c31c4349-193d-46d8-a0f9-e3e414e9409d
plot(
    tspan,
    [s1dot_vals s2dot_vals],
    xlabel = "Time (s)",
    ylabel = "Velocity along track (m/s)",
    label = ["s1_dot(t)" "s2_dot(t)"],
    linewidth = 2,
    title = "Piston Velocities vs Time"
)

# ╔═╡ eb01dc5a-77ee-412d-9468-1157ef8d4d36
plot(
    tspan,
    [s1ddot_vals s2ddot_vals],
    xlabel = "Time (s)",
    ylabel = "Acceleration along track (m/s^2)",
    label = ["s1_ddot(t)" "s2_ddot(t)"],
    linewidth = 2,
    title = "Piston Accelerations vs Time"
)

# ╔═╡ e44beb54-0152-47c5-ac2c-050eff89646c
md"""
	## Piston Kinematics In Global Coordinate System
	"""

# ╔═╡ bf6e093d-d926-4512-b2b0-ee67e8e7959b
begin
	function piston1_xy(s1)
	    return s1*cos(α1), s1*sin(α1)
	end
	function piston2_xy(s2)
	    return -s2*cos(α2), -s2*sin(α2)
	end
end

# ╔═╡ 6996a516-67aa-4297-b0f1-0580e064886a
begin
	function piston1_v_xy(s1dot)
	    return s1dot*cos(α1), s1dot*sin(α1)
	end
	function piston2_v_xy(s2dot)
	    return -s2dot*cos(α2), -s2dot*sin(α2)
	end
end

# ╔═╡ 16d56fb2-b4ba-4bb2-9d9f-04910d339a41
begin
	function piston1_a_xy(s1ddot)
	    return s1ddot*cos(α1), s1ddot*sin(α1)
	end
	function piston2_a_xy(s2ddot)
	    return -s2ddot*cos(α2), -s2ddot*sin(α2)
	end
end

# ╔═╡ 8c91c608-e929-45c9-9f45-5c9e89de1317
xp11,xp12 = piston1_xy(s1_vals)

# ╔═╡ 7c745e4b-8263-4e1f-969e-9e1d64ef3278
xp21,xp22 = piston2_xy(s2_vals)

# ╔═╡ 863f1020-cbc9-41eb-b251-54ba20a8c718
begin
	xv11,xv12 = piston1_v_xy(s1dot_vals)
	xv21,xv22 = piston2_v_xy(s2dot_vals)
end

# ╔═╡ ba0416bb-c88d-461b-a204-528476a7743b
begin
	xa11,xa12 = piston1_a_xy(s1ddot_vals)
	xa21,xa22 = piston2_a_xy(s2ddot_vals)
end

# ╔═╡ ad5a72a9-f54f-43d8-887f-60384e0eb72f
#Animation of the position of Piston 1 in the overall global coordinate system
begin
	displace_p1 = @animate for k in eachindex(tspan)
	    plot(
	        tspan,
	        [xp11, xp12];
	        xlabel = "Time (s)",
	        ylabel = "Position along track (m)",
	        label = ["X" "Y"],
	        linewidth = 2,
	        title = "Piston 1 Position vs Time"
	    )
	
	    scatter!([tspan[k]], [xp11[k]];
	             c=:dodgerblue, ms=6, label="")
	    scatter!([tspan[k]], [xp12[k]];
	             c=:tomato, ms=6, label="")
	end
	
	gif(displace_p1, "piston1_position_trace.gif"; fps=45)
	
end

# ╔═╡ c5c20310-9f64-438d-a246-2f0f06fafe92
#Animation of the position of Piston 2 in the overall global coordinate system
begin
	displace_p2 = @animate for k in eachindex(tspan)
	    plot(
	        tspan,
	        [xp21, xp22];
	        xlabel = "Time (s)",
	        ylabel = "Position along track (m)",
	        label = ["X" "Y"],
	        linewidth = 2,
	        title = "Piston 2 Position vs Time"
	    )
	
	    scatter!([tspan[k]], [xp21[k]];
	             c=:dodgerblue, ms=6, label="")
	    scatter!([tspan[k]], [xp22[k]];
	             c=:tomato, ms=6, label="")
	end
	
	gif(displace_p2, "piston1_position_trace.gif"; fps=45)
	
end

# ╔═╡ a5b189a8-a5c7-4a69-a4a6-53fb256b1f76
md"""
## Piston Velocity
"""

# ╔═╡ 4c938496-9204-4c15-8ffe-e6a8242f430b
begin
	velocity_p1 = @animate for k in eachindex(tspan)
	   plot(
		 tspan,
	 	[xv11, xv12];
	 	xlabel = "Time (s)",
	 	ylabel = "Velocity (m/s)",
	 	label = ["Xdot" "Ydot"],
	 	linewidth = 2,
	 	title = "Piston 1 Velocity vs Time"
 	)
	
	    scatter!([tspan[k]], [xv11[k]];
	             c=:dodgerblue, ms=6, label="")
	    scatter!([tspan[k]], [xv12[k]];
	             c=:tomato, ms=6, label="")
	end
	
	gif(velocity_p1, "piston1_velocity_trace.gif"; fps=45)
	
end

# ╔═╡ 6eba0cea-c34d-4905-b05b-55e8290ab6a7
begin
	velocity_p2 = @animate for k in eachindex(tspan)
	   plot(
		 tspan,
	 	[xv21, xv22];
	 	xlabel = "Time (s)",
	 	ylabel = "Velocity (m/s)",
	 	label = ["Xdot" "Ydot"],
	 	linewidth = 2,
	 	title = "Piston 2 Velocity vs Time"
 	)
	
	    scatter!([tspan[k]], [xv21[k]];
	             c=:dodgerblue, ms=6, label="")
	    scatter!([tspan[k]], [xv22[k]];
	             c=:tomato, ms=6, label="")
	end
	
	gif(velocity_p2, "piston2_velocity_trace.gif"; fps=45)
	
end

# ╔═╡ 10ed4dbe-5873-4091-9239-9b4c353e8783
md"""
## Acceleration
"""

# ╔═╡ 9dcb799e-91e2-41f3-bb90-f5c0ee48add6
begin
	accel_p1 = @animate for k in eachindex(tspan)
	   plot(
	 tspan,
	 [xa11, xa12];
	 xlabel = "Time (s)",
	 ylabel = "Acceleration (m/s^2)",
	 label = ["Xddot" "Yddot"],
	 linewidth = 2,
	 title = "Piston 1 Acceleration vs Time"
 	)
	
	    scatter!([tspan[k]], [xa11[k]];
	             c=:dodgerblue, ms=6, label="")
	    scatter!([tspan[k]], [xa12[k]];
	             c=:tomato, ms=6, label="")
	end
	
	gif(accel_p1, "piston1_accel_trace.gif"; fps=45)
	
end

# ╔═╡ 5711b475-6cf5-4c28-b4fe-87c40a92a881
begin
	accel_p2 = @animate for k in eachindex(tspan)
	   plot(
	 tspan,
	 [xa21, xa22];
	 xlabel = "Time (s)",
	 ylabel = "Acceleration (m/s^2)",
	 label = ["Xddot" "Yddot"],
	 linewidth = 2,
	 title = "Piston 2 Acceleration vs Time"
 	)
	
	    scatter!([tspan[k]], [xa21[k]];
	             c=:dodgerblue, ms=6, label="")
	    scatter!([tspan[k]], [xa22[k]];
	             c=:tomato, ms=6, label="")
	end
	
	gif(accel_p2, "piston2_accel_trace.gif"; fps=45)
	
end

# ╔═╡ c307baa6-eb57-4be8-b529-57be29344c9d
begin
	 figure_p1_x = plot(
		 tspan,
		 [xp11, xv11, xa11];
		 xlabel = "Time (s)",
		 ylabel = "Vector Value",
		 label = ["Position" "Velocity" "Acceleration"],
		 linewidth = 2,
		 title = "Piston 1 X"
	 )
	
	figure_p1_y =  plot(
		 tspan,
		 [xp12, xv12, xa12];
		 xlabel = "Time (s)",
		 ylabel = "Vector Value",
		 label = ["Position" "Velocity" "Acceleration"],
		 linewidth = 2,
		 title = "Piston 1 Y"
	 )
	plot(figure_p1_x,figure_p1_y, plot_title = "Piston 1 Kinematics")
end

# ╔═╡ 6e34c8c0-1b01-4425-b3bc-a52e94efb977
begin
	 figure_p2_x = plot(
		 tspan,
		 [xp21, xv21, xa21];
		 xlabel = "Time (s)",
		 ylabel = "Vector Value",
		 label = ["Position" "Velocity" "Acceleration"],
		 linewidth = 2,
		 title = "Piston 2 X"
	 )
	
	figure_p2_y =  plot(
		 tspan,
		 [xp22, xv22, xa22];
		 xlabel = "Time (s)",
		 ylabel = "Vector Value",
		 label = ["Position" "Velocity" "Acceleration"],
		 linewidth = 2,
		 title = "Piston 2 Y"
	 )
	plot(figure_p2_x,figure_p2_y, plot_title = "Piston 2 Kinematics")
end

# ╔═╡ 586cd0be-3bca-4338-a451-429cd6268414
md"""# System Rotation Animation Code"""

# ╔═╡ a354eb0a-91ea-4cbe-8bfb-6e0338d987eb
#Defines Channel Directions for Plots
begin
	channel1_direction = (cos(α1), sin(α1))
	channel2_direction = (cos(α2), sin(α2))  # crossed channels
end

# ╔═╡ edef31e2-ed59-4c67-a2fd-7ed2fe27834c
begin
	#Generates the Block Visual
	function rectangle_shape(cx, cy, dx, dy; length=0.04, width=0.02)
	    dir = [dx, dy] / norm([dx, dy])
	    nrm = [-dir[2], dir[1]]
	    hL, hW = length/2, width/2
	    pts = [ dir*hL+nrm*hW, dir*hL-nrm*hW,
	           -dir*hL-nrm*hW, -dir*hL+nrm*hW ]
	    Shape(cx .+ getindex.(pts,1), cy .+ getindex.(pts,2))
	end
	
	#Generates the slot visuals
	function slot_shape(cx, cy, dx, dy; half_length=0.25, half_width=0.025)
	    dir = [dx, dy] / norm([dx, dy])
	    nrm = [-dir[2], dir[1]]
	    ends = [-half_length*dir, half_length*dir]
	    pts = [ends[1]+half_width*nrm, ends[2]+half_width*nrm,
	           ends[2]-half_width*nrm, ends[1]-half_width*nrm]
	    Shape(cx .+ getindex.(pts,1), cy .+ getindex.(pts,2))
	end
end

# ╔═╡ 17c657dc-a2ad-4741-b75a-9b5f00526401
begin
	channel1 = slot_shape(0.0, 0.0, channel1_direction...; half_length=0.14)
	channel2 = slot_shape(0.0, 0.0, channel2_direction...; half_length=0.14)
end

# ╔═╡ 67941a28-6362-4735-a97a-c6484326c13d
begin
	time_s = tspan
	x1 = xp11; y1 = xp12
	x2 = xp21; y2 = xp22
	
	x_min = -0.15; x_max = 0.15
	y_min = -0.15; y_max = 0.15
	
	anim = @animate for k in eachindex(x1)
	    plot(; xlim=(x_min, x_max), ylim=(y_min, y_max), aspect_ratio=:equal,
	         legend=false, title="Mechanism motion  θ̇₃ = 2 rad/s  t=$(round(time_s[k], digits=3)) s")
	
	    plot!([x1[k], x2[k]], [y1[k], y2[k]]; lw=4)                 # connecting link
	    scatter!([x1[k]], [y1[k]]; ms=8)                             # piston 1
	    scatter!([x2[k]], [y2[k]]; ms=8)                             # piston 2
	end
	
	gif(anim, "mechanism.gif"; fps=60)
	``
end

# ╔═╡ 3464bcbe-9588-4fc1-aa50-5e11d0d01051
dt = tspan[2]-tspan[1]

# ╔═╡ 4e1db290-43a8-4552-99f2-e44a1f7f2186
gif(anim, "mechanism.gif", fps=1/dt)

# ╔═╡ dde15418-4f60-47cb-853b-c048422ceb08
begin
	anim3 = @animate for k in eachindex(x1)
	    plot(; aspect_ratio=:equal, legend=:topright,
	         xlim=(-0.35,0.35), ylim=(-0.35,0.35),
	         title="ω₃ = 2 rad/s   t=$(round(time_s[k],digits=1)) s")
	
	    plot!(channel1; c=:gray60, linecolor=:gray60, label= false)
	    plot!(channel2; c=:gray60, linecolor=:gray60, label= false)
	
	    piston1_shape = rectangle_shape(x1[k], y1[k], channel1_direction...)
	    piston2_shape = rectangle_shape(x2[k], y2[k], channel2_direction...)
	
	    plot!(piston1_shape; c=:dodgerblue, linecolor=:navy,
	          label = (k == 1 ? "Piston 1" : "Piston 1"))
	    plot!(piston2_shape; c=:tomato, linecolor=:maroon,
	          label = (k == 1 ? "Piston 2" : "Piston 2"))
	
	    plot!([x1[k], x2[k]], [y1[k], y2[k]]; lw=4, c=:black,
	          label = (k == 1 ? "Connecting bar" : "Connector Bar"))
	end
	
	gif(anim3, "mechanism_w_geometry.gif"; fps= 45)
	
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"

[compat]
Plots = "~1.41.4"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.12.5"
manifest_format = "2.0"
project_hash = "1767cefe1e3f3a0c2359842695780e9f15740bc6"

[[deps.AliasTables]]
deps = ["PtrArrays", "Random"]
git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
version = "1.1.3"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.2"

[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
version = "1.11.0"

[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
version = "1.11.0"

[[deps.BitFlags]]
git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.9"

[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1b96ea4a01afe0ea4090c5c8039690672dd13f2e"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.9+0"

[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "a21c5464519504e41e0cbc91f0188e8ca23d7440"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.18.5+1"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "962834c22b66e32aa10f7611c08c8ca4e20749a9"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.8"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "b0fd3f56fa442f81e0a47815c92245acfaaa4e34"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.31.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "67e11ee83a43eb71ddc950302c53bf33f0690dfe"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.12.1"
weakdeps = ["StyledStrings"]

    [deps.ColorTypes.extensions]
    StyledStringsExt = "StyledStrings"

[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
git-tree-sha1 = "8b3b6f87ce8f65a2b4f857528fd8d70086cd72b1"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.11.0"

    [deps.ColorVectorSpace.extensions]
    SpecialFunctionsExt = "SpecialFunctions"

    [deps.ColorVectorSpace.weakdeps]
    SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "37ea44092930b1811e666c3bc38065d7d87fcc74"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.13.1"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.3.0+1"

[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
git-tree-sha1 = "21d088c496ea22914fe80906eb5bce65755e5ec8"
uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
version = "2.5.1"

[[deps.Contour]]
git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.6.3"

[[deps.DataAPI]]
git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.16.0"

[[deps.DataStructures]]
deps = ["OrderedCollections"]
git-tree-sha1 = "e357641bb3e0638d353c4b29ea0e40ea644066a6"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.19.3"

[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
version = "1.11.0"

[[deps.Dbus_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl"]
git-tree-sha1 = "473e9afc9cf30814eb67ffa5f2db7df82c3ad9fd"
uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab"
version = "1.16.2+0"

[[deps.DelimitedFiles]]
deps = ["Mmap"]
git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
version = "1.9.1"

[[deps.DocStringExtensions]]
git-tree-sha1 = "7442a5dfe1ebb773c29cc2962a8980f47221d76c"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.9.5"

[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.7.0"

[[deps.EpollShim_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8a4be429317c42cfae6a7fc03c31bad1970c310d"
uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43"
version = "0.0.20230411+1"

[[deps.ExceptionUnwrapping]]
deps = ["Test"]
git-tree-sha1 = "d36f682e590a83d63d1c7dbd287573764682d12a"
uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4"
version = "0.1.11"

[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "27af30de8b5445644e8ffe3bcb0d72049c089cf1"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.7.3+0"

[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "95ecf07c2eea562b5adbd0696af6db62c0f52560"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.5"

[[deps.FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libva_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "01ba9d15e9eae375dc1eb9589df76b3572acd3f2"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "8.0.1+0"

[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
version = "1.11.0"

[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.5"

[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"]
git-tree-sha1 = "f85dac9a96a01087df6e3a749840015a0ca3817d"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.17.1+0"

[[deps.Format]]
git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc"
uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
version = "1.3.7"

[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "2c5512e11c791d1baed2049c5652441b28fc6a31"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.13.4+0"

[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7a214fdac5ed5f59a22c2d9a885a16da1c74bbc7"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.17+0"

[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll", "libdecor_jll", "xkbcommon_jll"]
git-tree-sha1 = "b7bfd56fa66616138dfe5237da4dc13bbd83c67f"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.4.1+0"

[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"]
git-tree-sha1 = "44716a1a667cb867ee0e9ec8edc31c3e4aa5afdc"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.73.24"

    [deps.GR.extensions]
    IJuliaExt = "IJulia"

    [deps.GR.weakdeps]
    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"

[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "be8a1b8065959e24fdc1b51402f39f3b6f0f6653"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.73.24+0"

[[deps.GettextRuntime_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll"]
git-tree-sha1 = "45288942190db7c5f760f59c04495064eedf9340"
uuid = "b0724c58-0f36-5564-988d-3bb0596ebc4a"
version = "0.22.4+0"

[[deps.Ghostscript_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Zlib_jll"]
git-tree-sha1 = "38044a04637976140074d0b0621c1edf0eb531fd"
uuid = "61579ee1-b43e-5ca0-a5da-69d92c66a64b"
version = "9.55.1+0"

[[deps.Glib_jll]]
deps = ["Artifacts", "GettextRuntime_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
git-tree-sha1 = "24f6def62397474a297bfcec22384101609142ed"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.86.3+0"

[[deps.Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8a6dbda1fd736d60cc477d99f2e7a042acfa46e8"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.15+0"

[[deps.Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[deps.HTTP]]
deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "PrecompileTools", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "5e6fe50ae7f23d171f44e311c2960294aaa0beb5"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.10.19"

[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll"]
git-tree-sha1 = "f923f9a774fcf3f5cb761bfa43aeadd689714813"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "8.5.1+0"

[[deps.InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
version = "1.11.0"

[[deps.IrrationalConstants]]
git-tree-sha1 = "b2d91fe939cae05960e760110b328288867b5758"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.2.6"

[[deps.JLFzf]]
deps = ["REPL", "Random", "fzf_jll"]
git-tree-sha1 = "82f7acdc599b65e0f8ccd270ffa1467c21cb647b"
uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
version = "0.1.11"

[[deps.JLLWrappers]]
deps = ["Artifacts", "Preferences"]
git-tree-sha1 = "0533e564aae234aff59ab625543145446d8b6ec2"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.7.1"

[[deps.JSON]]
deps = ["Dates", "Logging", "Parsers", "PrecompileTools", "StructUtils", "UUIDs", "Unicode"]
git-tree-sha1 = "b3ad4a0255688dcb895a52fafbaae3023b588a90"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "1.4.0"

    [deps.JSON.extensions]
    JSONArrowExt = ["ArrowTypes"]

    [deps.JSON.weakdeps]
    ArrowTypes = "31f734f8-188a-4ce0-8406-c8a06bd891cd"

[[deps.JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b6893345fd6658c8e475d40155789f4860ac3b21"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "3.1.4+0"

[[deps.JuliaSyntaxHighlighting]]
deps = ["StyledStrings"]
uuid = "ac6e5ff7-fb65-4e79-a425-ec3bc9c03011"
version = "1.12.0"

[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "059aabebaa7c82ccb853dd4a0ee9d17796f7e1bc"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.3+0"

[[deps.LERC_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "aaafe88dccbd957a8d82f7d05be9b69172e0cee3"
uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
version = "4.0.1+0"

[[deps.LLVMOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "eb62a3deb62fc6d8822c0c4bef73e4412419c5d8"
uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
version = "18.1.8+0"

[[deps.LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1c602b1127f4751facb671441ca72715cc95938a"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.3+0"

[[deps.LaTeXStrings]]
git-tree-sha1 = "dda21b8cbd6a6c40d9d02a73230f9d70fed6918c"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.4.0"

[[deps.Latexify]]
deps = ["Format", "Ghostscript_jll", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"]
git-tree-sha1 = "44f93c47f9cd6c7e431f2f2091fcba8f01cd7e8f"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.16.10"

    [deps.Latexify.extensions]
    DataFramesExt = "DataFrames"
    SparseArraysExt = "SparseArrays"
    SymEngineExt = "SymEngine"
    TectonicExt = "tectonic_jll"

    [deps.Latexify.weakdeps]
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"
    tectonic_jll = "d7dd28d6-a5e6-559c-9131-7eb760cdacc5"

[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.4"

[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "OpenSSL_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "8.15.0+0"

[[deps.LibGit2]]
deps = ["LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
version = "1.11.0"

[[deps.LibGit2_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "OpenSSL_jll"]
uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
version = "1.9.0+0"

[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "OpenSSL_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.11.3+1"

[[deps.Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
version = "1.11.0"

[[deps.Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "c8da7e6a91781c41a863611c7e966098d783c57a"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.4.7+0"

[[deps.Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "d36c21b9e7c172a44a10484125024495e2625ac0"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.7.1+1"

[[deps.Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "be484f5c92fad0bd8acfef35fe017900b0b73809"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.18.0+0"

[[deps.Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "97bbca976196f2a1eb9607131cb108c69ec3f8a6"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.41.3+0"

[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "f04133fe05eff1667d2054c53d59f9122383fe05"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.7.2+0"

[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "d0205286d9eceadc518742860bf23f703779a3d6"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.41.3+0"

[[deps.LinearAlgebra]]
deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
version = "1.12.0"

[[deps.LogExpFunctions]]
deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "13ca9e2586b89836fd20cccf56e57e2b9ae7f38f"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.29"

    [deps.LogExpFunctions.extensions]
    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"

    [deps.LogExpFunctions.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"

[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
version = "1.11.0"

[[deps.LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "f00544d95982ea270145636c181ceda21c4e2575"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "1.2.0"

[[deps.MacroTools]]
git-tree-sha1 = "1e0228a030642014fe5cfe68c2c0a818f9e3f522"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.16"

[[deps.Markdown]]
deps = ["Base64", "JuliaSyntaxHighlighting", "StyledStrings"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
version = "1.11.0"

[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"]
git-tree-sha1 = "8785729fa736197687541f7053f6d8ab7fc44f92"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.10"

[[deps.MbedTLS_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "ff69a2b1330bcb730b9ac1ab7dd680176f5896b8"
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.1010+0"

[[deps.Measures]]
git-tree-sha1 = "b513cedd20d9c914783d8ad83d08120702bf2c77"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.3"

[[deps.Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "ec4f7fbeab05d7747bdf98eb74d130a2a2ed298d"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.2.0"

[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"
version = "1.11.0"

[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2025.11.4"

[[deps.NaNMath]]
deps = ["OpenLibm_jll"]
git-tree-sha1 = "9b8215b1ee9e78a293f99797cd31375471b2bcae"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "1.1.3"

[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.3.0"

[[deps.Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b6aa4566bb7ae78498a5e68943863fa8b5231b59"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.6+0"

[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.29+0"

[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.7+0"

[[deps.OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "NetworkOptions", "OpenSSL_jll", "Sockets"]
git-tree-sha1 = "1d1aaa7d449b58415f97d2839c318b70ffb525a0"
uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.6.1"

[[deps.OpenSSL_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "3.5.4+0"

[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e2bb57a313a74b8104064b7efd01406c0a50d2ff"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.6.1+0"

[[deps.OrderedCollections]]
git-tree-sha1 = "05868e21324cede2207c6f0f466b4bfef6d5e7ee"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.8.1"

[[deps.PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.44.0+1"

[[deps.Pango_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"]
git-tree-sha1 = "0662b083e11420952f2e62e17eddae7fc07d5997"
uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
version = "1.57.0+0"

[[deps.Parsers]]
deps = ["Dates", "PrecompileTools", "UUIDs"]
git-tree-sha1 = "7d2f8f21da5db6a806faf7b9b292296da42b2810"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.8.3"

[[deps.Pixman_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"]
git-tree-sha1 = "db76b1ecd5e9715f3d043cec13b2ec93ce015d53"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.44.2+0"

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.12.1"
weakdeps = ["REPL"]

    [deps.Pkg.extensions]
    REPLExt = "REPL"

[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "41031ef3a1be6f5bbbf3e8073f210556daeae5ca"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.3.0"

[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "StableRNGs", "Statistics"]
git-tree-sha1 = "26ca162858917496748aad52bb5d3be4d26a228a"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.4.4"

[[deps.Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "TOML", "UUIDs", "UnicodeFun", "Unzip"]
git-tree-sha1 = "cb20a4eacda080e517e4deb9cfb6c7c518131265"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.41.6"

    [deps.Plots.extensions]
    FileIOExt = "FileIO"
    GeometryBasicsExt = "GeometryBasics"
    IJuliaExt = "IJulia"
    ImageInTerminalExt = "ImageInTerminal"
    UnitfulExt = "Unitful"

    [deps.Plots.weakdeps]
    FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
    GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
    ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254"
    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "07a921781cab75691315adc645096ed5e370cb77"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.3.3"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "8b770b60760d4451834fe79dd483e318eee709c4"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.5.2"

[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
version = "1.11.0"

[[deps.PtrArrays]]
git-tree-sha1 = "4fbbafbc6251b883f4d2705356f3641f3652a7fe"
uuid = "43287f4e-b6f4-7ad1-bb20-aadabca52c3d"
version = "1.4.0"

[[deps.Qt6Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"]
git-tree-sha1 = "d7a4bff94f42208ce3cf6bc8e4e7d1d663e7ee8b"
uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56"
version = "6.10.2+1"

[[deps.Qt6Declarative_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6ShaderTools_jll", "Qt6Svg_jll"]
git-tree-sha1 = "d5b7dd0e226774cbd87e2790e34def09245c7eab"
uuid = "629bc702-f1f5-5709-abd5-49b8460ea067"
version = "6.10.2+1"

[[deps.Qt6ShaderTools_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll"]
git-tree-sha1 = "4d85eedf69d875982c46643f6b4f66919d7e157b"
uuid = "ce943373-25bb-56aa-8eca-768745ed7b5a"
version = "6.10.2+1"

[[deps.Qt6Svg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll"]
git-tree-sha1 = "81587ff5ff25a4e1115ce191e36285ede0334c9d"
uuid = "6de9746b-f93d-5813-b365-ba18ad4a9cf3"
version = "6.10.2+0"

[[deps.Qt6Wayland_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6Declarative_jll"]
git-tree-sha1 = "672c938b4b4e3e0169a07a5f227029d4905456f2"
uuid = "e99dba38-086e-5de3-a5b1-6e4c66e897c3"
version = "6.10.2+1"

[[deps.REPL]]
deps = ["InteractiveUtils", "JuliaSyntaxHighlighting", "Markdown", "Sockets", "StyledStrings", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
version = "1.11.0"

[[deps.Random]]
deps = ["SHA"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
version = "1.11.0"

[[deps.RecipesBase]]
deps = ["PrecompileTools"]
git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.4"

[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"]
git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.6.12"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "1.0.1"

[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "62389eeff14780bfe55195b7204c0d8738436d64"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.1"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "9b81b8393e50b7d4e6d0a9f14e192294d3b7c109"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.3.0"

[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
version = "1.11.0"

[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[deps.SimpleBufferStream]]
git-tree-sha1 = "f305871d2f381d21527c770d4788c06c097c9bc1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.2.0"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
version = "1.11.0"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "64d974c2e6fdf07f8155b5b2ca2ffa9069b608d9"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.2.2"

[[deps.SparseArrays]]
deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
version = "1.12.0"

[[deps.StableRNGs]]
deps = ["Random"]
git-tree-sha1 = "4f96c596b8c8258cc7d3b19797854d368f243ddc"
uuid = "860ef19b-820b-49d6-a774-d7a799459cd3"
version = "1.0.4"

[[deps.Statistics]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.11.1"
weakdeps = ["SparseArrays"]

    [deps.Statistics.extensions]
    SparseArraysExt = ["SparseArrays"]

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "178ed29fd5b2a2cfc3bd31c13375ae925623ff36"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.8.0"

[[deps.StatsBase]]
deps = ["AliasTables", "DataAPI", "DataStructures", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "aceda6f4e598d331548e04cc6b2124a6148138e3"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.34.10"

[[deps.StructUtils]]
deps = ["Dates", "UUIDs"]
git-tree-sha1 = "28145feabf717c5d65c1d5e09747ee7b1ff3ed13"
uuid = "ec057cc2-7a8d-4b58-b3b3-92acb9f63b42"
version = "2.6.3"

    [deps.StructUtils.extensions]
    StructUtilsMeasurementsExt = ["Measurements"]
    StructUtilsTablesExt = ["Tables"]

    [deps.StructUtils.weakdeps]
    Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
    Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"

[[deps.StyledStrings]]
uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b"
version = "1.11.0"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.8.3+2"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
version = "1.11.0"

[[deps.TranscodingStreams]]
git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.11.3"

[[deps.URIs]]
git-tree-sha1 = "bef26fb046d031353ef97a82e3fdb6afe7f21b1a"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.6.1"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
version = "1.11.0"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
version = "1.11.0"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.Vulkan_Loader_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
version = "1.3.243+0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll"]
git-tree-sha1 = "96478df35bbc2f3e1e791bc7a3d0eeee559e60e9"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.24.0+0"

[[deps.XZ_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "9cce64c0fdd1960b597ba7ecda2950b5ed957438"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
version = "5.8.2+0"

[[deps.Xorg_libICE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a3ea76ee3f4facd7a64684f9af25310825ee3668"
uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
version = "1.1.2+0"

[[deps.Xorg_libSM_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libICE_jll"]
git-tree-sha1 = "9c7ad99c629a44f81e7799eb05ec2746abb5d588"
uuid = "c834827a-8449-5923-a945-d239c165b7dd"
version = "1.2.6+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "808090ede1d41644447dd5cbafced4731c56bd2f"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.13+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "aa1261ebbac3ccc8d16558ae6799524c450ed16b"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.13+0"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "6c74ca84bbabc18c4547014765d194ff0b4dc9da"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.4+0"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "52858d64353db33a56e13c341d7bf44cd0d7b309"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.6+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "1a4a26870bf1e5d26cd585e38038d399d7e65706"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.8+0"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "75e00946e43621e09d431d9b95818ee751e6b2ef"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "6.0.2+0"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "a376af5c7ae60d29825164db40787f15c80c7c54"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.8.3+0"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll"]
git-tree-sha1 = "0ba01bc7396896a4ace8aab67db31403c71628f4"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.7+0"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "6c174ef70c96c76f4c3f4d3cfbe09d018bcd1b53"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.6+0"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "7ed9347888fac59a618302ee38216dd0379c480d"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.12+0"

[[deps.Xorg_libpciaccess_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "4909eb8f1cbf6bd4b1c30dd18b2ead9019ef2fad"
uuid = "a65dc6b1-eb27-53a1-bb3e-dea574b5389e"
version = "0.18.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXau_jll", "Xorg_libXdmcp_jll"]
git-tree-sha1 = "bfcaf7ec088eaba362093393fe11aa141fa15422"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.1+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "ed756a03e95fff88d8f738ebc2849431bdd4fd1a"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.2.0+0"

[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "9750dc53819eba4e9a20be42349a6d3b86c7cdf8"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.6+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "f4fc02e384b74418679983a97385644b67e1263b"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll"]
git-tree-sha1 = "68da27247e7d8d8dafd1fcf0c3654ad6506f5f97"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "44ec54b0e2acd408b0fb361e1e9244c60c9c3dd4"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "5b0263b6d080716a02544c55fdff2c8d7f9a16a0"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.10+0"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "f233c83cad1fa0e70b7771e0e21b061a116f2763"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.2+0"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "801a858fc9fb90c11ffddee1801bb06a738bda9b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.7+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "00af7ebdc563c9217ecc67776d1bbf037dbcebf4"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.44.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a63799ff68005991f9d9491b6e95bd3478d783cb"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.6.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.3.1+2"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "446b23e73536f84e8037f5dce465e92275f6a308"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.7+1"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "c3b0e6196d50eab0c5ed34021aaa0bb463489510"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.14+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b6a34e0e0960190ac2a4363a1bd003504772d631"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.61.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "371cc681c00a3ccc3fbc5c0fb91f58ba9bec1ecf"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.13.1+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "125eedcb0a4a0bba65b657251ce1d27c8714e9d6"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.17.4+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.15.0+0"

[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
version = "0.2.2+0"

[[deps.libdrm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libpciaccess_jll"]
git-tree-sha1 = "63aac0bcb0b582e11bad965cef4a689905456c03"
uuid = "8e53e030-5e6c-5a89-a30b-be5b7263a166"
version = "2.4.125+1"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "56d643b57b188d30cccc25e331d416d3d358e557"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.13.4+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "646634dd19587a56ee2f1199563ec056c5f228df"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.4+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "91d05d7f4a9f67205bd6cf395e488009fe85b499"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.28.1+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "e015f211ebb898c8180887012b938f3851e719ac"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.55+0"

[[deps.libva_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll", "Xorg_libXext_jll", "Xorg_libXfixes_jll", "libdrm_jll"]
git-tree-sha1 = "7dbf96baae3310fe2fa0df0ccbb3c6288d5816c9"
uuid = "9a156e7d-b971-5f62-b2c9-67348b8fb97c"
version = "2.23.0+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"]
git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.8+0"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b4d631fd51f2e9cdd93724ae25b2efc198b059b1"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.7+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.64.0+1"

[[deps.p7zip_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.7.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.1+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e7b67590c14d487e734dcb925924c5dc43ec85f3"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "4.1.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "a1fc6507a40bf504527d0d4067d718f8e179b2b8"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.13.0+0"
"""

# ╔═╡ Cell order:
# ╟─f17103ea-06bf-11f1-a2b0-79e68ed152eb
# ╠═91f15f2c-7b4e-4f5f-8d45-9ebef77ce7dc
# ╟─b79f52a8-8c00-4b70-9fc5-164b7735e70d
# ╟─279da94d-6a6a-4884-bc51-09a7c90edafe
# ╟─a31c2198-98d0-4e79-ba9b-74487a3fd967
# ╟─891f182c-18f8-401d-a984-b1b3de2e67b0
# ╠═ea9a70e5-5790-4c11-97ae-690e6d9eb516
# ╠═fbe15d42-7162-4218-88e1-018ed677b3f0
# ╟─bcb494f9-a3df-46a7-9348-e2eac204e190
# ╠═b8e47bce-4ec8-4bf1-b64b-817e597a65b2
# ╟─2cddd741-e951-432e-9c5c-8853488d3c6d
# ╠═588c45c6-4633-4e7f-9534-57709602170f
# ╟─f09f7a94-7d0c-4485-ba10-be8f65eb456d
# ╠═f3004cb6-61b9-4eda-9472-8b313377577d
# ╟─b3151f63-6c9f-4bf9-ae4c-9fa89d6bc1c0
# ╠═a9ad74bb-1d7a-486c-a65c-295aaad37750
# ╠═735b0c96-cdb9-450e-a89d-1c76f2b15560
# ╠═6c4c1d6c-05c9-4eba-ad6b-57d74b94f1c3
# ╠═1f6e208c-e8bd-4974-9973-51b7d1a571f3
# ╠═b1bd29d2-aabe-490d-8e58-1854f2de485f
# ╠═0a8aec35-ae14-491c-9926-becdad7bbf46
# ╠═f4f50ebf-b7cc-4d13-be8f-90ea731502d5
# ╠═bcb7995f-2061-495b-8f1f-b134d5222c04
# ╠═66646852-6945-4a81-98aa-9ca3cd5b54dd
# ╠═d25d2756-1f09-46f4-80b3-96389c4eca6c
# ╟─1d0dcfeb-c2cc-4d09-88db-d6e9e430d7cc
# ╠═a6889fc8-bbac-473a-9abf-1276db8eb901
# ╟─2c48c51f-97ba-4c5c-aeed-afd29f735e65
# ╠═753ef8f1-c7e6-4728-ba19-69b852f108bb
# ╠═c31c4349-193d-46d8-a0f9-e3e414e9409d
# ╠═eb01dc5a-77ee-412d-9468-1157ef8d4d36
# ╟─e44beb54-0152-47c5-ac2c-050eff89646c
# ╠═bf6e093d-d926-4512-b2b0-ee67e8e7959b
# ╠═6996a516-67aa-4297-b0f1-0580e064886a
# ╠═16d56fb2-b4ba-4bb2-9d9f-04910d339a41
# ╠═8c91c608-e929-45c9-9f45-5c9e89de1317
# ╠═7c745e4b-8263-4e1f-969e-9e1d64ef3278
# ╠═863f1020-cbc9-41eb-b251-54ba20a8c718
# ╠═ba0416bb-c88d-461b-a204-528476a7743b
# ╠═ad5a72a9-f54f-43d8-887f-60384e0eb72f
# ╠═c5c20310-9f64-438d-a246-2f0f06fafe92
# ╟─a5b189a8-a5c7-4a69-a4a6-53fb256b1f76
# ╠═4c938496-9204-4c15-8ffe-e6a8242f430b
# ╠═6eba0cea-c34d-4905-b05b-55e8290ab6a7
# ╟─10ed4dbe-5873-4091-9239-9b4c353e8783
# ╠═9dcb799e-91e2-41f3-bb90-f5c0ee48add6
# ╠═5711b475-6cf5-4c28-b4fe-87c40a92a881
# ╠═c307baa6-eb57-4be8-b529-57be29344c9d
# ╠═6e34c8c0-1b01-4425-b3bc-a52e94efb977
# ╟─586cd0be-3bca-4338-a451-429cd6268414
# ╠═a354eb0a-91ea-4cbe-8bfb-6e0338d987eb
# ╠═edef31e2-ed59-4c67-a2fd-7ed2fe27834c
# ╠═17c657dc-a2ad-4741-b75a-9b5f00526401
# ╠═67941a28-6362-4735-a97a-c6484326c13d
# ╠═3464bcbe-9588-4fc1-aa50-5e11d0d01051
# ╠═4e1db290-43a8-4552-99f2-e44a1f7f2186
# ╠═dde15418-4f60-47cb-853b-c048422ceb08
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002