Chapter 8.4, Problem 1E

Interpretation Introduction

Interpretation:

To sketch the waveforms of $\text{x}\left(\text{t}\right)$ and $\text{y}\left(\text{t}\right)$ for the system $\dot{\text{r}}\text{ = r}\left({\text{1 - r}}^{\text{2}}\right)$, $\dot{\text{θ}}\text{ = μ - sin θ}$, for $\text{μ}$ slightly greater than $\text{1}$.

Concept Introduction:

Cartesian coordinates can be converted to Polar coordinates by

$\text{x = r cos θ}$, $\text{y = r sin θ}$

Polar coordinates can be converted to Cartesian coordinates by

$\text{r = }\sqrt{{\text{x}}^{\text{2}}{\text{ + y}}^{\text{2}}}$, ${\text{θ = tan}}^{\text{-1}}\left(\frac{\text{y}}{\text{x}}\right)$