I have written some code to generate a gif for the double pendulum problem:
# In another code not shown here, I've:
# - computed solution of double pendulum problem
# - extracted independent variables θ₁, θ₂ from solution
N = length(θ₁)
# plot configuration space, i.e. a torus
Θ₁ = -π:0.01:π
Θ₂ = -π:0.01:π
X_torus = [(1 + cos(Θ₂ᵢ)) * cos(Θ₁ᵢ) for Θ₁ᵢ in Θ₁, Θ₂ᵢ in Θ₂]
Y_torus = [(1 + cos(Θ₂ᵢ)) * sin(Θ₁ᵢ) for Θ₁ᵢ in Θ₁, Θ₂ᵢ in Θ₂]
Z_torus = [sin(Θ₂ᵢ) for Θ₁ᵢ in Θ₁, Θ₂ᵢ in Θ₂]
p₂ = surface(X_torus, Y_torus, Z_torus, colorbar = :none, legend = false, xlims = [-2, 2], ylims = [-2, 2], zlims = [-2, 2])
# create gif
anim = @animate for i = 2:200:N
# plot first pendulum
i_ = max(1, i-1000)
x1 = @. cos(θ₁[i_:i] - π/2)
y1 = @. sin(θ₁[i_:i] - π/2)
x₁ = x1[end]
y₁ = y1[end]
α = range(0.0, 1.0, length = length(x1))
p₁ = plot(x1, y1, α = α, color = 1, legend = false, xlims = [-2, 2], ylims = [-2, 2])
# plot second pendulum
x2 = @. x1 + cos(θ₂[i_:i] - π/2)
y2 = @. y1 + sin(θ₂[i_:i] - π/2)
x₂ = x2[end]
y₂ = y2[end]
plot!(p₁, x2, y2, color = 3, α = α, xlabel = L"x", ylabel = L"y")
plot!(p₁, [0; x₁], [0; y₁], linewidth = 3, color = :black)
plot!(p₁, [x₁; x₂], [y₁; y₂], linewidth = 3, color = :black)
scatter!(p₁, (0, 0), markersize = 5, markercolor = :black)
scatter!(p₁, (x₁, y₁), markersize = 5, markercolor = 1)
scatter!(p₁, (x₂, y₂), markersize = 5, markercolor = 3)
# get torus' plot
p₃ = deepcopy(p₂)
# plot path of representative particle in configuration space
X = @. (1 + cos(θ₁[i_:i])) * cos(θ₂[i_:i])
Y = @. (1 + cos(θ₁[i_:i])) * sin(θ₂[i_:i])
Z = @. sin(θ₁[i_:i])
plot!(p₃, X, Y, Z, color = :black)
scatter!(p₃, (X[end], Y[end], Z[end]), markersize = 5, markercolor = :black)
plot(p₁, p₃, size = (600, 300))
end
gif(anim, "double-pendulum.gif")
On the left, the actual double pendulum; on the right, the trajectory traced by a representative “particle” over its configuration space (i.e. a torus parametrised by \theta_1 and \theta_2). My problem is that such a trajectory always goes in front of the torus, whereas it should sometimes go behind. What am I doing wrong? Am I missing some option for plot? Is this a Plots or a GR issue?