Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 3.5, Problem 5E
Interpretation Introduction

Interpretation:

To estimate the time scale Tfast in terms of original dimensional quantities m, g, r, ω, and b. Rescale the original differential equation using Tfast as the characteristics time, and determine the term which is negligible on this time scale. Show that Tfast<< Tslow if ε << 1.

Concept Introduction:

Express the equation in dimension less form.

Nondimensionalize and simplify the equation to reduce the number of parameters.

Rescale the original equation using characteristic time scale.

Write balance force equation and set the time scale.

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