Chapter 7.3, Problem 8E

Interpretation Introduction

Interpretation:

The phase portrait of ${\dot{\text{r}}\text{ = r(1 - r}}^{\text{2}}\text{) + μrcosθ}$, $\dot{\text{θ}}\text{ = 1}$ for various values of $\text{μ > 0}$ is to be drawn. Also, if critical value ${\text{μ}}_{\text{c}}$ exists at which the closed orbit ceases to exist, it is to be estimated, and if such ${\text{μ}}_{\text{c}}$ does not exist, then it is to be proved that closed orbit exists for all $\text{μ > 0}$.

Concept Introduction:

Critical point of the system is the point at which $\dot{\text{r}}\text{ = 0}\text{.}$