Chapter 7.1, Problem 9E

Interpretation Introduction

Interpretation:

A pair of differential equations is to be derived for the path of the dog and the system is to be analyzed. Whether the dog ever catches the duck is to be determined as well asa pair of differential equations is to be derived for the path of the dog if dog swims k times faster than the duck. Also, what does dog end up doing in the long run if $\text{k = }\frac{\text{1}}{\text{2}}$ is to be obtained?

Concept Introduction:

The expression for the resultant vector between $\text{A}$ and $\text{B}$ is,

$\text{R = }\sqrt{{\text{A}}^{\text{2}}{\text{+ B}}^{\text{2}}\text{+2 AB cosθ}}$

A limit cycle is an isolated closed trajectory means the neighboring trajectories are not closed.

These are nonlinear systems.