I'm looking to see how I can plot the following ODE orbit:

$\phi(t) =\begin{pmatrix} \sin(2t) \\ \cos(t) \end{pmatrix} $

The author of my ODE textbook has recommended that I use a vector plot. The textbook has an example for

VectorPlot[{y, −Sin[x]}, {x, −2π, 2π}, {y, −5, 5}]

To plot the above orbit, would I do a vector plot similar to

VectorPlot[{Sin[2t], Cos[t]}, {x, −2π, 2π}, {y, −5, 5}]

This doesn't appear to work when I test it in Wolfram|Alpha.

  • $\begingroup$ Any reference to the book? $\endgroup$ – zhk Nov 10 '18 at 4:21
  • $\begingroup$ I included the book as a hyperlink. The book is ODE by Teschl. He goes through the VectorPlot in chapter 6.2. $\endgroup$ – Axion004 Nov 10 '18 at 4:23
  • 1
    $\begingroup$ Notice the example used functions of x and y given ranges of x and y. Then you want to plot functions of t given ranges of x and y. Can you see the disconnect? This VectorPlot[{Sin[2 x], Cos[y]}, {x, -2 Pi, 2 Pi}, {y, -5, 5}] will plot using WolframAlpha, but I cannot be certain that is exactly what you want. Can you turn what you want to functions of x and y? Or turn everything into a function of t? $\endgroup$ – Bill Nov 10 '18 at 5:14
  • $\begingroup$ Yes, set $x(t)=sin(2t)$ and $y(t)=cos(t)$. This would produce a two dimensional system for $\frac{dx}{dt} = f(x(t),y(t))$ and $\frac{dy}{dt} = g(x(t),y(t))$. The phase plot of the system could be drawn by ParametricPlot[{Sin[2 t], Cos[t]}, {t, -50, 50}]. $\endgroup$ – Axion004 Nov 10 '18 at 18:56

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.