Project_02-12

### A Pluto.jl notebook ###
# v0.20.21

using Markdown
using InteractiveUtils

# ╔═╡ 4cb60cfa-b688-4298-af98-d20ed38728e2
using Symbolics, ModelingToolkit, DifferentialEquations, Plots, Latexify, NLsolve

# ╔═╡ 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
"""

# ╔═╡ 829e8d21-126c-4fde-acba-bb7ef4f19a06
md"""
# Things That Need to be Done

* Fix up the acceleration math because I think there's a cleaner way to solve there rather than doing one step, reshaping, then another very strangely.
* add more parametric cases
* Improve animation to look closer to the problem statement image (larger tracks, actual blocks and bar, etc.)
* Whatever else you guys want to come up with (:
"""

# ╔═╡ 0d9be664-d7c5-4084-add2-25e5418742d6
md""" 
# Generalized Coordinates
To start we identify our set of generalized coordinates. Since we have $3$ bodies in planar space, we will have $9$ coordinates, $R_x^1$, $R_y^1$, $\theta^1$, $R_x^2$, $R_y^2$, $\theta^2$, and $R_x^3$, $R_y^3$, $\theta^3$. 

So our generalized coordinate vector $q$ is:

$q = \begin{bmatrix} 
R_x^1 &
R_y^1 &
\theta^1 &
R_x^2 &
R_y^2 &
\theta^2 &
R_x^3 &
R_y^3 &
\theta^3
\end{bmatrix}^T$

"""

# ╔═╡ ff4cce5d-0823-46f8-b28e-24735797eb31
begin
	@independent_variables t
	@parameters l3 theta3_rate slot_center_x slot_center_y slot_angle1 slot_angle2 theta3_0
	@variables q[1:9] q_dot[1:9]

    const Rx1=1; const Ry1=2; const theta1=3
    const Rx2=4; const Ry2=5; const theta2=6
    const Rx3=7; const Ry3=8; const theta3=9
	
	params = [l3, theta3_rate, slot_center_x, slot_center_y, slot_angle1, slot_angle2, theta3_0]

    n1x = -sin(slot_angle1); n1y =  cos(slot_angle1)  # normal to track 1
    n2x = -sin(slot_angle2); n2y =  cos(slot_angle2)  # normal to track 2
end

# ╔═╡ 8ee16c64-3111-44e5-86e6-3731cfbe753a
md"""
We have $3$ pre-defined coordinate systems, $X^1Y^1$, $X^2Y^2$, and $X^3Y^3$. We will define the origin of the reference coordinate system $X^0Y^0$ as the center of the intersections of the two slots, such that the later math is simpler.
"""

# ╔═╡ 24ac663e-cde4-4b70-879f-a42be1dc67ac
md"""
# Constraints

In this system we have to account for the following constraints:

* Pin Joints $A$ and $B$ for the connections between body $1$ and $3$, and $2$ and $3$ respectively. This produces $4$ constraint equations since pins restrict relative translation.

* Prismatic Joints $C$ and $D$ for the sliding motion between bodies $1$ and $2$ and their respective slots. This produces $4$ constraint equations since prismatic joints restrict rotation and translation perpendicular to the axis.

* The driven constraint given as $\dot{\theta^3}=2 ~ rad/s$. This produces $1$ constraint equation.


With these constraints we will have $n=3n_b= 9 = n_c$, and thus, our system is Kinematically Driven.


"""

# ╔═╡ c9b67bfa-0866-4f70-9594-6e8cb1dbdb69
md"""
## Pin Joints

For pin joint $A$, we know that point $A^1$ must have the same global position as $A^3$:

$r_A^1 - r_A^3 = 0$

$R^1 + A^1 \bar{u}_A^1 - R^3 - A^3 \bar{u}_A^3 = 0$
$\begin{bmatrix} R_x^1 \\ R_y^1\end{bmatrix} + \begin{bmatrix} \cos\theta^1 & -\sin\theta^1 \\ \sin\theta^1 & \cos\theta^1 \end{bmatrix} \begin{bmatrix} 0 \\ 0\end{bmatrix} -  \begin{bmatrix} R_x^3 \\ R_y^3\end{bmatrix} - \begin{bmatrix} \cos\theta^3 & -\sin\theta^3 \\ \sin\theta^3 & \cos\theta^3 \end{bmatrix} \begin{bmatrix} -\frac{l_3}{2} \\ 0\end{bmatrix} = \begin{bmatrix} 0 \\ 0\end{bmatrix}$

This results in the following two constraint equations:

$\begin{cases}
R_x^1 - R_x^3 + \frac{l_3}{2}\cos\theta^3 = 0 \\
R_y^1 - R_y^3 + \frac{l_3}{2}\sin\theta^3 = 0 
\end{cases}$
"""

# ╔═╡ 7f826175-5309-4557-b70a-98661fa2db0b
md"""
For pin joint $B$, we know that point $B^2$ must have the same global position as $B^3$, and so similarly to joint $A$ we derive the following equations:

$r_A^1 - r_A^3 = 0$

$R^2 + A^2 \bar{u}_B^2 - R^3 - A^3 \bar{u}_B^3 = 0$
$\begin{bmatrix} R_x^2 \\ R_y^2\end{bmatrix} + \begin{bmatrix} \cos\theta^2 & -\sin\theta^2 \\ \sin\theta^2 & \cos\theta^2 \end{bmatrix} \begin{bmatrix} 0 \\ 0\end{bmatrix} -  \begin{bmatrix} R_x^3 \\ R_y^3\end{bmatrix} - \begin{bmatrix} \cos\theta^3 & -\sin\theta^3 \\ \sin\theta^3 & \cos\theta^3 \end{bmatrix} \begin{bmatrix} \frac{l_3}{2} \\ 0\end{bmatrix} = \begin{bmatrix} 0 \\ 0\end{bmatrix}$

This results in the following two constraint equations:

$\begin{cases}
R_x^2 - R_x^3 - \frac{l_3}{2}\cos\theta^3 = 0 \\
R_y^2 - R_y^3 - \frac{l_3}{2}\sin\theta^3 = 0 
\end{cases}$
"""

# ╔═╡ 5dfe5714-16be-4a2e-baf5-799f1d7aa46b
md"""
## Prismatic Constraints

There are $2$ constraints produced for each prismatic constraint on blocks $1$ and $2$. Firstly, the two blocks must stay at a constant relative orientation, so this produces the following $2$ constraint equations:

$\begin{cases}
\theta^1 - \alpha_1 = 0 \\
\theta^2 - \alpha_2 = 0
\end{cases}$


The unit direction vector of a slot with angle α is defined as  
**u(α) = [cos(α), sin(α)]**, and the corresponding unit normal vector is **n(α) = [-sin(α), cos(α)]**.

The slot intersection point is **r_c = [slot_center_x, slot_center_y]**, and the slider position vectors are **r₁ = [q[Rx1], q[Ry1]]**, **r₂ = [q[Rx2], q[Ry2]]**.

The prismatic constraints are enforced by requiring zero displacement
perpendicular to each slot axis:
**C_pris1 = n(slot_angle1)ᵀ · (r₁ − r_c) = 0**,  
**C_pris2 = n(slot_angle2)ᵀ · (r₂ − r_c) = 0**.

We can determine the constants $\alpha_1$ and $\alpha_2$ by analyzing the orientation of each slots angle. Since each of the tracks are at $\pm 45^\circ$, $\theta_1=45^\circ$ and $\theta_2=-45^\circ$.

$\begin{cases}
\theta^1 - \frac{\pi}{4} = 0 \\
\theta^2 + \frac{\pi}{4} = 0
\end{cases}$

Next we need to ensure neither block can move perpendicular to it's track's axis. To do this we check that the dot product between the displacement of the block $r$ with respect to the center of the two tracks, and the normal vector corresponding to each blocks track $n$ is $0$. This corresponds to no component of displacement for either block being in the direction of the perpendicular axis, meaning the blocks only move along their respective tracks. Mathmatically we represent this as:

$\begin{cases}
{n^1}^T r^{1,slot}=0 \\
{n^2}^T r^{2,slot}=0
\end{cases}$

Since we define the origin of our global coordinate system at the center of our slots, $r_slot$, the displacement vectors simply become the global position vectors of each block. To determine the normal vectors for each block, we take the angle each corresponding track is at, and take the vector $\begin{bmatrix} \cos(\theta+\pi/2) & \sin(\theta+\pi/2) \end{bmatrix}^T$. This is a normal vector relative to each track. Thus our axis constraints are:

$\begin{cases}
\begin{bmatrix} \cos(\frac{\pi}{4} + \frac{\pi}{2}) \\ \sin(\frac{\pi}{4} + \frac{\pi}{2})\end{bmatrix} \begin{bmatrix}R_x^1 \\ R_y^1\end{bmatrix}=0 \\
\begin{bmatrix} \cos(-\frac{\pi}{4} + \frac{\pi}{2}) \\ \sin(-\frac{\pi}{4} + \frac{\pi}{2})\end{bmatrix} \begin{bmatrix}R_x^2 \\ R_y^2\end{bmatrix}=0
\end{cases}$

Which becomes after expanding the trig and matrix multiplications, and dividing by a common factor:

$\begin{cases}
-R_x^1 + R_y^1 = 0 \\
R_x^2 + R_y^2 = 0
\end{cases}$
"""

# ╔═╡ 0ca25147-769e-481b-a60f-67bae630f75b
md"""
## Driven Constraint

The driven constraint in the problem is given as $\dot{\theta^3} - \omega_3 = 0$, where $\omega_3=2 ~ rad/s$ We can integrate the expression to obtain the constraint.

$\int_0^t \dot{\theta^3}-\omega_3 ~ dt = \int_0^t 0 ~ dt$

This becomes the constraint:

$\theta^3 - \frac{\pi}{2} - \omega_3t = 0$

We use $\frac{\pi}{2}$ as $\theta^3_0$ since this is what's shown in the problem image.
"""

# ╔═╡ 6f5245e4-973c-4927-b814-c4de5f3648d7
md"""
## Constraint Matrix

We can now construct our constraint matrix in the form $C(q, t) = 0$.

$C(q,t)=\begin{bmatrix}
R_x^1 - R_x^3 + \frac{l_3}{2}\cos\theta^3 \\
R_y^1 - R_y^3 + \frac{l_3}{2}\sin\theta^3 \\
R_x^2 - R_x^3 - \frac{l_3}{2}\cos\theta^3 \\
R_y^2 - R_y^3 - \frac{l_3}{2}\sin\theta^3 \\
\theta^1 - \frac{\pi}{4} \\
\theta^2 + \frac{\pi}{4} \\
-R_x^1 + R_y^1 \\
R_x^2 + R_y^2 \\
\theta^3 - \theta^3_0 - \omega_3t 
\end{bmatrix} = \begin{bmatrix} 0\\0\\0\\0\\0\\0\\0\\0\\0\end{bmatrix}$
"""

# ╔═╡ fb181be8-310b-4482-8444-ae07aae08ebc
begin 
	C = [
        q[Rx1] - q[Rx3] + (l3/2)*cos(q[theta3]);
        q[Ry1] - q[Ry3] + (l3/2)*sin(q[theta3]);
        q[Rx2] - q[Rx3] - (l3/2)*cos(q[theta3]);
        q[Ry2] - q[Ry3] - (l3/2)*sin(q[theta3]);
        
		# piston orientations align to slot
        q[theta1] - slot_angle1;
        q[theta2] - slot_angle2;

		 # slider 1 on line through (slot_center_x, slot_center_y) at angle slot_angle1
        n1x*(q[Rx1] - slot_center_x) + n1y*(q[Ry1] - slot_center_y);
		
		# slider 2 on line through (slot_center_x, slot_center_y) at angle slot_angle2
        n2x*(q[Rx2] - slot_center_x) + n2y*(q[Ry2] - slot_center_y);
		
        # rotation of the rigid bar (const)
        q[theta3] - (theta3_0 + theta3_rate*t)
		
    	]
end

# ╔═╡ 83878f28-707b-4920-838f-503e83528e7a
begin 
	Cq = Symbolics.jacobian(C, q)
	Ct = Symbolics.derivative(C, t)
	
	# Acceleration RHS derivation (consistent with many multibody texts):
	# Cq*qdd = Qd where Qd = - (∂/∂q(Cq*qdot)*qdot + 2*∂Cq/∂t*qdot + ∂Ct/∂t)
	temp1 = Cq * q_dot
	temp1_col = Symbolics.Array(reshape(collect(temp1), 9, 1))
	temp2 = Symbolics.jacobian(temp1_col, q)
	
	Qd1 = Symbolics.Array(reshape(collect(-temp2*q_dot), 9))
	Qd2 = Symbolics.Array(reshape(collect(-2*Symbolics.derivative(Cq, t)*q_dot), 9))
	Qd3 = -Symbolics.derivative(Ct, t)
	Qd  = Qd1 + Qd2 + Qd3
end

# ╔═╡ ce27d36f-1564-415d-9b34-201b238d87cb
begin 
	# Position constraints f(q,p,t) = C(q,p,t)
	C_func  = build_function(C,  q, params, t; expression=Val(false))[1]
		
	# Jacobian Cq(q,p)
	Cq_func = build_function(Cq, q, params; expression=Val(false))[1]
		
	# Time term Ct(q,p,t)
	Ct_func = build_function(Ct, q, params, t; expression=Val(false))[1]
		
	# Qd(q, qdot, p, t)
	Qd_func = build_function(Qd, q, q_dot, params, t; expression=Val(false))[1]
end

# ╔═╡ 3f56e210-5a55-4a6b-a48d-37dbd9318fa4
function compute_positions(parameter_values; nsteps=250)
    # unpack parameters (just for readable internal logic)
    bar_length, bar_rate, center_x, center_y, a1, a2, a3_0 = parameter_values
	
    t_final = 2π / max(abs(bar_rate), 1e-9)
    time_samples = range(0.0, t_final, length=nsteps)
	
    # initial guess: place sliders slightly along each track from the intersection
    direction1 = [cos(a1), sin(a1)]
    direction2 = [cos(a2), sin(a2)]
    slider1_xy = [center_x, center_y] .+ 0.05 .* direction1
    slider2_xy = [center_x, center_y] .+ 0.05 .* direction2
    bar_center_xy = 0.5 .* (slider1_xy .+ slider2_xy)
	
    q_guess = Float64[
        slider1_xy[1], slider1_xy[2], a1,
        slider2_xy[1], slider2_xy[2], a2,
        bar_center_xy[1], bar_center_xy[2], a3_0
    ]
	
    positions = Vector{Vector{Float64}}()
	
    # NLsolve residual wrapper
    function f_factory(t_now)
        return function f!(F, x)
            F[:] = C_func(x, parameter_values, t_now)
        end
    end
	
    for t_now in time_samples
        f! = f_factory(t_now)
        sol = nlsolve(f!, q_guess; method=:trust_region)
		
        sol.f_converged || error("Position solve failed at t=$t_now, 
residual=$(sol.residual_norm)")
		
        q_guess = sol.zero
        push!(positions, copy(q_guess))
    end
	
    return positions, time_samples
end

# ╔═╡ 264ca81d-612c-4ea9-98cf-df9fb8235899
md"""
## Velocity Analysis

We can differentiate the constraint matrix with respect to time to get:

$\frac{d}{dt}C(q,t) = C_q (q,t) \dot{q} + C_q (q,t) = 0$

So we can solve the following system for velocities.

$C_q\dot{q} = C_t$
"""

# ╔═╡ c8384dee-1f8f-4a4b-bf92-02c9580c72e5
function compute_velocities(positions, time_samples, parameter_values)
    velocities = Vector{Vector{Float64}}()
    for (q_now, t_now) in zip(positions, time_samples)
        jac = Cq_func(q_now, parameter_values)
        rhs = Ct_func(q_now, parameter_values, t_now)
        push!(velocities, -(jac \ rhs))
    end
    return velocities
end

# ╔═╡ b512cb1e-6683-43b4-8908-622e5715d32a
md"""
## Acceleration Analysis
To find acceleration we differentiate the expression for velocity.

$C_q(q,t)\,\ddot{q} = Q_d(q,\dot{q},t)$

where 

$Q_d = -\left(\frac{\partial}{\partial q}(C_q\dot{q})\dot{q} + 2\frac{\partial C_q}{\partial t}\dot{q} + \frac{\partial C_t}{\partial t}\right).$

"""

# ╔═╡ eb4a86c2-f82b-4e05-8ce2-a4b8f124919a
# Computes qdd from: Cq*qdd = Qd
function compute_accelerations(positions, velocities, time_samples, parameter_values)
    accelerations = Vector{Vector{Float64}}()
    for (q_now, v_now, t_now) in zip(positions, velocities, time_samples)
        jac = Cq_func(q_now, parameter_values)
        rhs = Qd_func(q_now, v_now, parameter_values, t_now)
        push!(accelerations, vec(jac \ rhs))
    end
    return accelerations
end

# ╔═╡ 58a80f26-d769-460d-bcd2-e0fc4e19a240
# Returns positions, velocities, accelerations, time_samples
function compute_values(parameter_values; nsteps=250)
    positions, time_samples = compute_positions(parameter_values; nsteps=nsteps)
    velocities = compute_velocities(positions, time_samples, parameter_values)
    accelerations = compute_accelerations(positions, velocities, time_samples, parameter_values)
    return positions, velocities, accelerations, time_samples
end

# ╔═╡ b0f4221f-f9a9-4097-8483-2f2b998c8a2d
function plot_coupler_traces(case_names, all_positions)
    plt = plot(title="Body 3 Coupler Trace (Rx3 vs Ry3)",
               xlabel="Rx3 (m)", ylabel="Ry3 (m)",
               aspect_ratio=:equal, legend=:topright)
    for (i, positions) in enumerate(all_positions)
        pos_mat = hcat(positions...)'
        plot!(plt, pos_mat[:, Rx3], pos_mat[:, Ry3], lw=2, label=case_names[i])
    end
    return plt
end

# ╔═╡ 551c32a3-aaa5-4c72-b3a0-c315b8e74e4b
function plot_time_histories(case_names, all_positions, all_times)
    plt = plot(layout=(2,1), size=(950,650), legend=:topright)
    for (i, positions) in enumerate(all_positions)
        pos_mat = hcat(positions...)'
        tvals = all_times[i]
        plot!(plt[1], tvals, pos_mat[:, Rx3], lw=2, label=case_names[i],
              title="Rx3 vs Time", xlabel="t (s)", ylabel="Rx3 (m)")
        plot!(plt[2], tvals, pos_mat[:, Ry3], lw=2, label=case_names[i],
              title="Ry3 vs Time", xlabel="t (s)", ylabel="Ry3 (m)")
    end
    return plt
end

# ╔═╡ 7b7c175a-9e9d-4096-9795-89be14e390d3
function animate_double_slider(positions, parameter_values; filename=nothing, fps=30)
    _, _, xc, yc, a1, a2, _ = parameter_values
    direction1 = (cos(a1), sin(a1))
    direction2 = (cos(a2), sin(a2))
	
    lim = 0.20
    s = range(-lim, lim, length=120)
	
    x3_hist = Float64[]
    y3_hist = Float64[]
	
    anim = @animate for qv in positions
        push!(x3_hist, qv[Rx3]); push!(y3_hist, qv[Ry3])
		
        plot(xlim=(xc-lim, xc+lim), ylim=(yc-lim, yc+lim),
             aspect_ratio=:equal, legend=false,
             title="Double Slider Crank (Parameterized)")
		
        plot!(xc .+ s .* direction1[1], yc .+ s .* direction1[2], c=:black, lw=3)
        plot!(xc .+ s .* direction2[1], yc .+ s .* direction2[2], c=:black, lw=3)
		
        plot!([qv[Rx1], qv[Rx2]], [qv[Ry1], qv[Ry2]], c=:blue, lw=4)
        scatter!([qv[Rx1]],[qv[Ry1]], c=:red, ms=6)
        scatter!([qv[Rx2]],[qv[Ry2]], c=:green, ms=6)
        scatter!([qv[Rx3]],[qv[Ry3]], c=:black, ms=5)
        plot!(x3_hist, y3_hist, ls=:dash, lw=2, c=:purple)
    end

	return filename === nothing ? gif(anim; fps=fps) : gif(anim, filename; fps=fps)
end

# ╔═╡ e75c61bc-36ac-4d42-aa91-4c80ce5a3d47
md"""
## Cases
"""

# ╔═╡ 96a1dcb1-2566-4945-9272-be330949011f
begin 
# Common baseline
bar_rate = 2.0
center_x = 0.0
center_y = 0.0
theta3_initial = π/2
	
# (1) Large l3
case_large_l3 = [0.20, bar_rate, center_x, center_y,  π/4, -π/4, theta3_initial]
	
# (2) Short l3
case_short_l3 = [0.05, bar_rate, center_x, center_y,  π/4, -π/4, theta3_initial]
	
# (3) Small angle + big angle
case_small_big_angles = [0.10, bar_rate, center_x, center_y, deg2rad(10), deg2rad(80), 
theta3_initial]
	
case_names = ["Large l3", "Short l3", "Small/Big Angles"]
case_params = [case_large_l3, case_short_l3, case_small_big_angles]
	
# Solve all cases
nsteps = 250
all_positions = Vector{Vector{Vector{Float64}}}(undef, length(case_params))
all_times     = Vector{Any}(undef, length(case_params))
end 

# ╔═╡ 66611e71-3895-4e8b-8754-a48f7626068f
for (i, p) in enumerate(case_params)
    positions, velocities, accelerations, time_samples = compute_values(p; 
nsteps=nsteps)
    all_positions[i] = positions
    all_times[i] = time_samples
end

# ╔═╡ 464f3061-6238-4f84-b339-9f1b150e7ae6
md"""
## Plotting
"""

# ╔═╡ e079f3d4-2711-4d3d-be7a-004eff45ba3e
begin 
	coupler_plot = plot_coupler_traces(case_names, all_positions)
	time_plot    = plot_time_histories(case_names, all_positions, all_times)
	
	display(coupler_plot)
	display(time_plot)
end

# ╔═╡ cc203892-c0da-4a6d-97bd-e73e100fe3c8
# Animations (writes files in working directory)
for (i, p) in enumerate(case_params)
	safe = replace(case_names[i], " "=>"_", "/"=>"_")
	animate_double_slider(all_positions[i], p; filename="double_slider_"*safe*".gif", fps=30)
end

# ╔═╡ 3624494a-640e-42a1-86c3-d1cd349803f9
begin
displayed_gifs = Any[]
	for (i, p) in enumerate(case_params)
		safe = replace(case_names[i], " "=>"_", "/"=>"_")
		push!(displayed_gifs, animate_double_slider(all_positions[i], p; 	
													filename="double_slider_$safe.gif",
													fps=30))
	end
	displayed_gifs
end

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Plots = "~1.41.5"
Symbolics = "~7.8.0"
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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 = "e2a7072fc0cdd7949528c1455a3e5da4122e1153"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.56+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.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
git-tree-sha1 = "1350188a69a6e46f799d3945beef36435ed7262f"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2022.0.0+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
# ╠═4cb60cfa-b688-4298-af98-d20ed38728e2
# ╟─829e8d21-126c-4fde-acba-bb7ef4f19a06
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# ╠═ff4cce5d-0823-46f8-b28e-24735797eb31
# ╟─8ee16c64-3111-44e5-86e6-3731cfbe753a
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# ╟─c9b67bfa-0866-4f70-9594-6e8cb1dbdb69
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# ╠═fb181be8-310b-4482-8444-ae07aae08ebc
# ╠═83878f28-707b-4920-838f-503e83528e7a
# ╠═ce27d36f-1564-415d-9b34-201b238d87cb
# ╠═3f56e210-5a55-4a6b-a48d-37dbd9318fa4
# ╟─264ca81d-612c-4ea9-98cf-df9fb8235899
# ╠═c8384dee-1f8f-4a4b-bf92-02c9580c72e5
# ╟─b512cb1e-6683-43b4-8908-622e5715d32a
# ╠═eb4a86c2-f82b-4e05-8ce2-a4b8f124919a
# ╠═58a80f26-d769-460d-bcd2-e0fc4e19a240
# ╠═b0f4221f-f9a9-4097-8483-2f2b998c8a2d
# ╠═551c32a3-aaa5-4c72-b3a0-c315b8e74e4b
# ╠═7b7c175a-9e9d-4096-9795-89be14e390d3
# ╟─e75c61bc-36ac-4d42-aa91-4c80ce5a3d47
# ╠═96a1dcb1-2566-4945-9272-be330949011f
# ╠═66611e71-3895-4e8b-8754-a48f7626068f
# ╟─464f3061-6238-4f84-b339-9f1b150e7ae6
# ╠═e079f3d4-2711-4d3d-be7a-004eff45ba3e
# ╠═cc203892-c0da-4a6d-97bd-e73e100fe3c8
# ╠═3624494a-640e-42a1-86c3-d1cd349803f9
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002