I got to a point where I have $x$ and $y$ coordinates of a position vector written as a function of time.

y[t_]:= Sin[t] t^4 + 5 t^2;

Now my idea was to somehow use Manipulate[] so that I could animate how the position of point $(x(t),y(t))$ changes in a two-dimensional space with time.

I was able to use Manipulate and plot $x$ or $y$ coordinates separately but I can't get any further. I got an idea to discretize the time domain and than use Manipulate with combination of ListPlot or something, yet I would like to stay in the continuous case if possible.

  • $\begingroup$ See e.g. this answer Finding unit tangent, normal, and binormal vectors for a given r(t) wher you'll find a 3D visualization. You should find a specific questions on this site, I guess it is a duplicate. $\endgroup$
    – Artes
    Commented Mar 19, 2016 at 16:55
  • $\begingroup$ You can use ListPlot[{{x[t],y[t]}}] for plotting a single point in 2d space. $\endgroup$
    – Oscillon
    Commented Mar 19, 2016 at 19:54

1 Answer 1


Do you mean something like this?

x[t_] := t^2 - 67;
y[t_] := Sin[t] t^4 + 5 t^2;
 Graphics[Arrow[{{0, 0}, {x[t], y[t]}}], Axes -> True], {t, 0, 3}]

I did it like this because you wanted the position. However, I suggest something that not only you can see the current position, but the plot has the memory of previous positions:

 ParametricPlot[{x[t], y[t]}, {t, 0, tmax}], {tmax, 0.01, 3}]
  • $\begingroup$ Yes, this is what I needed! $\endgroup$
    – skrat
    Commented Mar 20, 2016 at 8:19

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.