Classical Mechanics (Kibble & Berkshire) · Problem 8.16

The energy principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · van-der-pol-numerical

Problem

Van der Pol's equation A classic non-linear oscillation equation that has a limit cycle is Van der Pol's equation

\ddot{x} + \epsilon\left(x^2 - 1\right)\dot{x} + x = 0,

where

\epsilon

is a positive parameter. Solve the equation numerically with

\epsilon = 2

(say) and plot the motion of a few of the phase points in the

(x, v)

-plane. All the phase paths tend to the limit cycle. One can see the same effect in a different way by plotting the solution function

x(t)

against

t