Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 12.4, Problem 1E
Interpretation Introduction

Interpretation:

To prove time delay trajectory for the following figure traces an ellipse for 0<τ<π2

Nonlinear Dynamics and Chaos, Chapter 12.4, Problem 1E

Concept Introduction:

  • The general format of the ellipse equation is

    Ax2+ Bxy + Cy2+ Dx + Ey + F = 0

    A, B, C, D, E, F are constants and (x,y) is a set of points.

  • The condition for non-degenerate real ellipse is,

    B24AC<0 and

    C|AB2D2B2CE2D2E2F|=CΔ<0

    If CΔ>0, ellipse is imaginary, and if Δ=0, then ellipse is a point.

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