Animating Particle Motion Using Parametric Plot and Animate

Question

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?

Answer 1

• Method-1: Using MeshFunctions -> {#4 &}, MeshStyle -> {AbsolutePointSize[10], 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[10], 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}]

Answer 2

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]}]`