DynamicModule with Animate

*To*: mathgroup at smc.vnet.net*Subject*: [mg113570] DynamicModule with Animate*From*: Hugh Goyder <h.g.d.goyder at cranfield.ac.uk>*Date*: Wed, 3 Nov 2010 02:54:03 -0500 (EST)

The working DynamicModule below shows an acoustic wave in a pipe with a side branch. By changing the length of the side branch or the wavelength you can see reflected waves, transmitted waves and standing waves. The positive pressure is shown in red and the negative pressure in brown. The problem is that I want to do more complicated pipework and this animation is on the limit of what I can show. In version 7 on my machine it is jerky and I can't seem to make AnimationRate make it smoother. I am trying to isolate the animation from the dynamic variables by wrapping the Animate in its own Dynamic. I would be happy for the frames of the animation to be made first, all stored and then have Animate show them. There would be a delay when the new wavelength is selected and the frames built but I don't mind this if I get a smooth animation of the system. It seems that Animate is recalculating each frame as it goes and this is slowing down the animation. How can I simulate far more complex systems? Many thanks Hugh Goyder DynamicModule[{f1, f2, f3, lam = 2.666, L = 2, a1, a2, a3, col, sf = 0.1, inc = 0.1}, f1[t_, lam_, L_, x_] := 1/(101 + 99 Cos[4 L Pi/lam]) ( Cos[t + 2 Pi x/lam] (-1 + Cos[4 L Pi/lam]) + Cos[t - 2 Pi x/lam] (101 + 99 Cos[4 L Pi/lam]) + 10 Sin[t + 2 Pi x/lam] Sin[4 L Pi/lam]); f2[t_, lam_, L_, x_] := 1/(101 + 99 Cos[4 L Pi/lam]) ( 10 (9 Cos[t + 2 Pi (L - x)/lam] + 11 Cos[t - 2 Pi (L + x)/lam]) Cos[2 L Pi/lam]); f3[t_, lam_, L_, x_] := 1/(101 + 99 Cos[4 L Pi/lam]) ( 20 Cos[2 Pi (L - x)/lam] (10 Cos[t] Cos[2 L Pi/lam] + Sin[t] Sin[2 L Pi/lam])); Column[{ Row[{"L", Slider[Dynamic[L], {0, 5}], Dynamic[L]}], Row[{"lam", Slider[Dynamic[lam], {0, 5}], Dynamic[lam]}], Dynamic[ Animate[Graphics3D[{ Line[{{-5, 0, 0}, {5, 0, 0}}], Line[{{0, 0, 0}, {0, 0, L}}], Table[a1 = sf f1[t, lam, L, x]; If[a1 > 0, col = Red, col = Brown]; {col, Line[Table[{x, a1 Cos[theta], a1 Sin[theta]}, {theta, 0, 2 Pi, Pi/4.}]]}, {x, -5, 0, inc}], Table[a2 = sf f2[t, lam, L, x]; If[a2 > 0, col = Red, col = Brown]; {col, Line[Table[{x, a2 Cos[theta], a2 Sin[theta]}, {theta, 0, 2 Pi, Pi/4.}]]}, {x, 0, 5, inc}], Table[a3 = sf f3[t, lam, L, x]; If[a3 > 0, col = Red, col = Brown]; {col, Line[Table[{ a3 Cos[theta], a3 Sin[theta], x}, {theta, 0, 2 Pi, Pi/4.}]]}, {x, 0, L, inc}] }, Boxed -> False, ImageSize -> 7 72, PlotRange -> {{-6, 6}, {-1, 1}, {-1, 6}} ], {t, 0, 2 Pi}]] }] ]