Chapter 6.5, Problem 15E

Interpretation Introduction

Interpretation:

To show that the equation can be nondimensionalizedto $\varphi \text{" = sin }\varphi \left(\text{cos}\varphi {\text{ - γ}}^{\text{-1}}\right)$. Draw all the qualitative different phase portraits as $\text{γ}$ varies. What do the phase portraits imply about the physical motion of the bead?

Concept Introduction:

A conserved quantity is a real-valued continuous function that is constant on trajectories.

A conservative system does not have any attracting fixed points.

The parametric curves traced by solutions of a differential equation are known as trajectories.

The geometrical representation of a collection of trajectories in a phase plane is called a phase portrait.