Manipulate showing the trajectory of a particle along a parametric curve

Question

I have a particle which follows a certain trajectory given by rx and ry

rx = E0*q*(-T*w*Cos[T* w] + Sin[T* w])/(2*m*w^2)
ry = E0*q*(-1 + Cos[T*w] + T*w]*Sin[T* w])/(2*m*w^2)

I am able to plot rx and ry but I need to have an animation of a particle (a point) which follows this path from T = 0 to T = 10 microsec. Here is the code.:

Manipulate[
  ParametricPlot[{
      (E0*q*1.6*10^-19*(-T*ω*Cos[T*ω] + Sin[T*ω]))/(2*m*1.6*10^-27*ω^2), 
      (E0*q*1.6*10^-19*(-1 + Cos[T*ω] + T*ω*Sin[T*ω]))/(2*m*1.6*10^-27*ω^2)
    },
    {T, 0, temp}, 
    AxesLabel -> {Row[{Style["rx", Italic], " (cm)"}], Row[{Style["ry", Italic], " (cm)"}]},
    PerformanceGoal -> "Quality", 
    Epilog -> {
      PointSize[0.04], 
      Point[{
        (E0*q*1.6*10^-19*(-temp*ω*Cos[temp*ω] + Sin[temp*ω]))/(2*m*1.6*10^-27*ω^2), 
        (E0*q*1.6*10^-19*(-1 + Cos[temp*ω] + temp*ω*Sin[temp*ω]))/(2*m*1.6*10^-27*ω^2)
      }]
  }], 
  Style["horizontal", Bold], 
  {{m, 1, "mass"}, 1, 4, 1, ImageSize -> Tiny, Appearance -> "Labeled"}, 
  {{ω, 200*2*π*1000, "frequency"}, 200*2*π*1000, 400*2*π*1000, 1*2*π*1000, 
    ImageSize -> Tiny, Appearance -> "Labeled"}, 
  {{E0, 40, "amplitude"}, 40, 80, 1, ImageSize -> Tiny, Appearance -> "Labeled"}, 
  {{q, 1, "charge"}, 1, 7, 1, ImageSize -> Tiny, Appearance -> "Labeled"},
  Delimiter,
  {{temp, 1*10^-6, "pulselength"}, 10^10 - 6, 20*10^-6, 10*10^-6, ControlType -> Trigger},
  ControlPlacement -> Left]

Any help will be appreciated.

Answer 1

I haven't looked at your code closely, but perhaps you can use the following approach:

Manipulate[
 ParametricPlot[
  {4 Sin[t] Cos[t], 3 Cos[t]}, 
  {t, 0, 2 Pi},
  PerformanceGoal -> "Quality",
  Epilog -> {Red,
    PointSize -> .05,
    Point[{4 Sin[anotherT] Cos[anotherT], 3 Cos[anotherT]}]}],
 {{anotherT, 0}, 0, 2 Pi, Pi/64,
  ControlType -> Trigger}
 ]