46 lines
1.9 KiB
Text
46 lines
1.9 KiB
Text
using Luxor
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using Colors
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using BoundaryValueDiffEq
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# constants for differential equations and movie
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const g = 9.81
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const L = 1.0 # pendulum length in meters
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const bobd = 0.10 # pendulum bob diameter in meters
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const framerate = 50.0 # intended frame rate/sec
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const t0 = 0.0 # start time (s)
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const tf = 2.3 # end simulation time (s)
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const dtframe = 1.0/framerate # time increment per frame
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const tspan = LinRange(t0, tf, Int(floor(tf*framerate))) # array of time points in animation
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const bgcolor = "black" # gif background
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const leaderhue = (0.80, 0.70, 0.20) # gif swing arm hue light gold
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const hslcolors = [HSL(col) for col in (distinguishable_colors(
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Int(floor(tf*framerate)+3),[RGB(1,1,1)])[2:end])]
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const giffilename = "pendulum.gif" # output file
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# differential equations
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simplependulum(du, u, p, t) = (θ=u[1]; dθ=u[2]; du[1]=dθ; du[2]=-(g/L)*sin(θ))
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bc2(residual, u, p, t) = (residual[1] = u[end÷2][1] + pi/2; residual[2] = u[end][1] - pi/2)
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bvp2 = BVProblem(simplependulum, bc2, [pi/2,pi/2], (tspan[1],tspan[end]))
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sol2 = solve(bvp2, MIRK4(), dt=dtframe) # use the MIRK4 solver for TwoPointBVProblem
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# movie making background
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backdrop(scene, framenumber) = background(bgcolor)
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function frame(scene, framenumber)
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u1, u2 = sol2.u[framenumber]
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y, x = L*cos(u1), L*sin(u1)
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sethue(leaderhue)
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poly([Point(-4.0, 0.0), Point(4.0, 0.0),
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Point(160.0x,160.0y)], :fill)
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sethue(Colors.HSV(framenumber*4.0, 1, 1))
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circle(Point(160.0x,160.0y), 160bobd, :fill)
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text(string("frame $framenumber of $(scene.framerange.stop)"),
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Point(0.0, -190.0),
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halign=:center)
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end
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muv = Movie(400, 400, "Pendulum Demo", 1:length(tspan))
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animate(muv, [Scene(muv, backdrop),
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Scene(muv, frame, easingfunction=easeinoutcubic)],
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creategif=true, pathname=giffilename)
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