Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 4.4, Problem 1E
Interpretation Introduction

Interpretation:

To find the conditions under which it is valid to approximate the equation mL2θ¨ + bθ˙ + mgL sin θ = Γ by its overdamped limit bθ˙ + mgL sin θ = Γ.

Concept Introduction:

If Γ is the constant torque applied on a pendulum, then its general equation is given by

mL2θ¨ + bθ˙ + mgL sin θ = Γ, where

m is the mass of the pendulum, L is the length of the pendulum, b is a viscous damping constant, and g is the acceleration due to gravity.

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