Classical Dynamics of Particles and Systems · Problem 4-22

Gravitation — Marion & Thornton

Physics — Mechanics · nonlinear-inductor-poincare

Problem

A circuit with a nonlinear inductor can be modeled by the first-order differential equations

\frac{dx}{dt} = y

\frac{dy}{dt} = -ky - x^3 + B\cos t

Chaotic oscillations for this situation have been extensively studied. Use a computer to construct the Poincaré section plot for the case

k = 0.1

and

9.8 \leq B \leq 13.4

. Describe the map.