# Animating Particle Motion Using Parametric Plot and Animate

I am attempting to animate my parametric plot and add a particle to move on the line but I am having difficulties. Here is my graph for the trajectory:

Manipulate[ParametricPlot3D[{v t, v γ Sin[θ t], v γ Cos[θ t]}, {t, 0, 20}], {v, 0,
2π}, {γ,0,2π}, {θ, 0, 2π}]


I want to have a circle that follows the path and here's my attempt at writing the animate code.

Animate[Show[
[ParametricPlot3D[{v t, v γ Sin[θ t], v γ Cos[θ t]}, {t, 0, 20}],
Graphics[{Red, Disk[{v t, v γ Sin[θ t]}, 0.2]}]], {v,
0, 2π}, {γ, 0, 2π}, {θ, 0, 2π}]


I think that I messed up in the Graphics part but I am not sure how to add the parameters so that the particle can move along the line. Any suggestions? Could someone tell me what is going wrong?

• "Disk" contains "t" that is defined in "ParametricPlot". Further, you can not simply combine 2D and 3D Graphics. Feb 13 at 18:09

• Method-1: Using MeshFunctions -> {#4 &}, MeshStyle -> {AbsolutePointSize, Red}, Mesh -> {{a}}, Method -> {"BoundaryOffset" -> False}]
Animate[ParametricPlot3D[{v t, v γ Sin[θ t],
v γ Cos[θ t]}, {t, 0, a}, MeshFunctions -> {#4 &},
MeshStyle -> {AbsolutePointSize, Red}, Mesh -> {{a}},
Method -> {"BoundaryOffset" -> False}], {a, $MachineEpsilon, 20}, {v, 0, 2 π}, {γ, 0, 2 π}, {θ, 0, 2 π}]  • Method-2: Change the arrow style. Animate[ParametricPlot3D[{v t, v γ Sin[θ t], v γ Cos[θ t]}, {t, 0, a}] /. Line[a_] -> {Arrowheads[{{.01, 1, {Graphics3D[{Red, Sphere[]}], 1}}}], Arrow[a]}, {a,$MachineEpsilon, 20}, {v, 0, 2 π}, {γ,
0, 2 π}, {θ, 0, 2 π}] I don't how to add particle to the path but, ı'm generally using arrows instead of trying to add particles.

Animate[ParametricPlot3D[{v t, v \[Gamma] Sin[\[Theta] t],
v \[Gamma] Cos[\[Theta] t]}, {t, 0, a}] /. Line -> Arrow, {a, 0, 20}, {v, 0, 2 \[Pi]}, {\[Gamma], 0, 2 \[Pi]}, {\[Theta], 0, 2 \[Pi]}]
`