Classical Mechanics (Kibble & Berkshire) · Problem 8.12

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

Physics — Mechanics · poincare-bendixson-van-der-pol

Problem

Van der Pol's equation Use Poincar\'e--Bendixson to show that Van der Pol's equation x¨+ϵx˙(x2−1)+x=0,\ddot{x} + \epsilon \dot{x}\left(x^2 - 1\right) + x = 0, has a limit cycle for any positive value of the constant ϵ\epsilon. [The method is similar to that used for Rayleigh's equation in Example 8.4.]

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