Creating an animation for time evolution of the path of a particle

Question

Suppose a particle has the following path

ParametricPlot[{2 (θ - π/2) + 2*Cos[θ], 
  2*(1 - Sin[θ])}, {θ, π/2, 4*π + π/2}]

which looks like this

I want to make an animation of the curve. In fact, if we consider the particle as a blue dot, inside the 2D plane. Then as $\theta$ evolves the blue dot which indicates the particle should follow the path according to the equations and thus leaving a solid line behind it. I tried this

Manipulate[
 ParametricPlot[{2 (θ - π/2) + 2*Cos[θ], 
   2*(1 - Sin[θ])}, {θ, π/2, θmax}], {θmax, π/2, 4*π + π/2}]

but it is not working! Why?

What is a simple way to do this?

@J.M.: I did exactly the same thing with Manipulate instead of Animate in kglr's answer but it didn't work! Let me change the question to this issue. — Hosein Rahnama, Jan 24 '17 at 09:28
Fixing the PlotRange and making a small offset to the starting point helps quite a bit (you'll notice a similar strategy being used in the answers of the question I linked to): Manipulate[ParametricPlot[(* stuff *), {θ, π/2 - $MachineEpsilon, θmax}, PlotRange -> {{0, 8 π}, {0, 4}}], (* stuff *)]. — J. M.'s missing motivation, Jan 24 '17 at 09:43

score 1 · Answer 1 · edited Jan 24 '17 at 10:15

1

A quick demo of Animate:

f[θ_] := {2 (θ - π/2) + 2*Cos[θ], 2*(1 - Sin[θ])}

Animate[
 ParametricPlot[f[θ], {θ, π/2, θmax}, 
  PlotRange -> {{0, 8 π}, {0, 4}}, PlotStyle -> Opacity[0.5],
  Epilog -> {Point[f[θmax]]}
  ],
 {θmax, π/2, 4*π + π/2}
 ]

edited Jan 24 '17 at 10:15

Mr.Wizard

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answered Jan 24 '17 at 09:29

Quantum_Oli

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Creating an animation for time evolution of the path of a particle

1 Answers1