Here it is: Roughly the animation I wanted to create. A harmonic oscillator, with the corresponding trajectory in phase space and a bead-on-wire projection of the trajectory onto the potential energy curve.
I wanted to insert this in a powerpoint slide I would be using for an online lecture, so an animated GIF seemed like a good option. I started with an example from Dirk Mittler’s blog. (link no longer working)
What I really wanted to do was include several axes like in these examples from my earlier post at TheMaximalist, which created multiple scenes using several calls to gr2d() and then drew the scenes in a single call to draw(). The trouble I encountered was that the collection of time-synchronized multiple scenes weren’t rendered simultaneously in the animated GIF — the animation flickered back and forth between the scenes.
So I turned off the axes and made my own triplet of axes in a single scene using parametric lines and including the needed vertical offsets.
One key thing that took me a while to find: In my Windows installation (Maxima 5.44 and wxMaxima 20.06.6), no matter what I specified for a path in the file_name argument to draw(), the animated GIF file ended up getting written in C:\maxima-5.44.0
I’ve pasted the code below.
scenes: $ for i:0 thru 61 do ( scenes: append(scenes, [gr2d(proportional_axes=xy, noframe, ytics=false,xtics=false,nticks=100, /* oscillator 2 units below */ color=black, parametric(t,-2,t,-1.2,1.2), /* phase space 2 units above */ color=black, parametric(t,0,t,-1.2,1.2), parametric(0,t,t,-1.2,1.2), color=blue, parametric(cos(t),sin(t),t,0,2*%pi), /* potential */ color=black, parametric(t,2,t,-1.2,1.2), parametric(0,2+t,t,-.1,1), color=blue, explicit(2+x^2,x,-1.2,1.2), color=red,point_type=filled_circle, points([cos(i/10),cos(i/10),cos(i/10)],[-2,-sin(i/10),2+cos(i/10)^2]))] ) )$ draw( delay = 10, file_name = "oscillator_phasespace_potential", terminal = 'animated_gif, scenes )$