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I am trying to represent the motion of a particle along a given trajectory. So I defined the following functions

x[t_] := Cos[t]

y[t_] := Sin[t]

T[t_] := {x[t], y[t]}

Trajectory = ParametricPlot[T[t], {t, 0, 2*Pi}, ImageSize -> Large,AspectRatio -> 1];

P[t_] := Point[T[t]]

V[t_] = Arrow[{T[t], T[t] + {x'[t], y'[t]}}];

and so I give the command

Animate[Show[Trajectory, Graphics[V[t], P[t]]], {t, 0, 2*Pi}]

but unfortunately the final result is really stranger and moreover I do not see the point P in the motion but only the velocity vectors and the trajectory that strangely changes its size. So could someone help me, please?

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  • $\begingroup$ If you indend by 4spaces your code is shown (I edited your question accordingly) $\endgroup$
    – Ulrich Neumann
    Nov 22, 2021 at 15:31
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    $\begingroup$ Fix Show by adding PlotRange and wrapping V[t] and P[t] into a list: Show[Trajectory, Graphics[{V[t], P[t]}], PlotRange -> {{-2, 2}, {-2, 2}}]. $\endgroup$
    – Domen
    Nov 22, 2021 at 15:36
  • $\begingroup$ @UlrichNeumann Okay, thanks for the edit. $\endgroup$
    – Antonio Maria Di Mauro
    Nov 22, 2021 at 15:36
  • $\begingroup$ @Domen Okay, it works for a circumference but strangely it does not work for a parabol, e.g. try to put x[t_]:=t, y[t_]:=t^2. $\endgroup$
    – Antonio Maria Di Mauro
    Nov 22, 2021 at 15:43
  • $\begingroup$ @Domen E.g. see this x[t_] := t y[t_] := t^2 T[t_] := {x[t], y[t]} Trajectory = ParametricPlot[T[t], {t, 0, 5}, ImageSize -> Large, AspectRatio -> 1]; P[t_] := Point[T[t]] V[t_] = Arrow[{T[t], T[t] + {x'[t], y'[t]}}]; Animate[Show[Trajectory, Graphics[{V[t], P[t]}], PlotRange -> {{0, 25}, {0, 25}}], {t, 0, 5}] $\endgroup$
    – Antonio Maria Di Mauro
    Nov 22, 2021 at 15:46

1 Answer 1

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Try

Trajectory =ParametricPlot[T[t], {t, 0, 2*Pi}, ImageSize -> Large,AspectRatio -> 1, PlotRange -> 1.5 {{-1, 1}, {-1, 1}}];

P[t_] := Point[T[t]]

V[t_] := Arrow[{T[t], T[t] + {x'[t], y'[t]}}];

Animate[Show[{Trajectory, Graphics[{V[t], P[t]}, PlotRange -> 1.5 {{-1, 1}, {-1, 1}}]}, ImageSize -> 300], {t, 0, 2*Pi}]

enter image description here

The same algorithm works for any possible motion: anyway the value of t in Trajectory and in Animate must be only one and moreover the PlotRange in Animate must be adjusted conveniently

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