Chapter 4.1, Problem 7E

Interpretation Introduction

Interpretation:

To find and classify all the fixed points of the vector field $\dot{\text{θ}}\text{ = sin kθ}$, where $\text{k}$ is a positive integer. To sketch the phase portrait on the circle.

Concept Introduction:

The vector field on the circle can be represented by $\dot{\text{θ}}\text{ = f(θ)}$.

Fixed points are the points where $\dot{\text{θ}}\text{ = 0}$.