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differential equations - Simulate a polygon bouncing with collision detection inside a circle/polygon






the example can be see in help page by searching WhenEvent;


ball2d[r_?NumericQ] := Reap@NDSolveValue[{{x'[t] == vx[t], y'[t] == vy[t], x1'[t] == vx[t], 

y1'[t] == vy[t]}, WhenEvent[{x[t]^2 + y[t]^2 == 1, x1[t]^2 + y1[t]^2 == .9}, {x1[t] ->

x[t] + (pp = RandomReal[.1]), y1[t] -> y[t] + Sqrt[0.02 - pp^2], vy[t] -> -.9 vy[t],

vx[t] -> -.9 vx[t]}],x[0] == 0, y[0] == 0, x1[0] == .1, y1[0] == .1, vx[0] == 1,


vy[0] == 1}, {x[t], y[t], x1[t], y1[t]}, {t, 0, 200},DiscreteVariables -> {vx, vy}];

{sol1, v} = ball2d[4/3];

Manipulate[ ParametricPlot[#, {t, 0, [Tau]}, Frame -> True, PlotRange -> 2,

PlotPoints -> 10, PlotStyle -> Thickness[0.02],Epilog -> {PointSize[.05], Point[# /. (t -> [Tau])],

ContourPlot[{x^2 + y^2 == 1}, {x, -1, 1}, {y, -1, 1}][[1]]}] & /@


Partition[sol1, 2], {{[Tau], 11.9}, 0.01, 198}, SaveDefinitions -> True]

The following example show a stick bouncing inside a circle, not so good


What's the right way?


How can I go forward to replace the stick with a triangle or a polygon? and futher a polygon3d?


Any examples?


Manipulate[ ParametricPlot[#, {t, 0, [Tau]}, Frame -> True, PlotRange -> 2, 

PlotPoints -> 10, PlotStyle -> Thickness[0.0001],Epilog -> {Pink, Thick,


Line[{{#[[1]], #[[2]]}, {#[[3]], #[[4]]}}] /. (t -> [Tau]), ContourPlot[{x^2 + y^2 == 1}, {x, -1, 1}, {y, -1, 1}][[1]]}] &@

sol1, {{[Tau], 0.01}, 0.01, 198, .1}, SaveDefinitions -> True]

enter image description here


The reference posted by Mr.Wizard is about a point model which is much simpler. My question is about extending the example in WhenEvent help page. However the animation is really shown by that example, can you image a stick bouncing like that?




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