Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 7.6, Problem 9E
Interpretation Introduction

Interpretation:

To calculate the averaged equations and to analyze the long-term behavior of the system x¨ + x + ε h(x, x˙) = 0, where h(x, x˙) = (x2- 1)x˙3. To find the amplitude and frequency of any limit cycles for the original system. If possible, to solve the averaged equations explicitly for x(t, ε), given the initial conditions x(0) = a, x˙(0)=0.

Concept Introduction:

The averaged or slow-time equations are given by r = h sin θ, rϕ = h cos θ.

The common solution of the system is given by x0 = r(T) cos(ϕ(T)+τ).

The explicit solution is specifiedas x(t, ε) = x0+ O(ε).

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