Chapter 6.5, Problem 14E

Interpretation Introduction

Interpretation:

To show that ${\text{v}}^{\text{3}}\text{-3vcosθ}$ is a conserved quantity. Sketch the phase portrait for ${\dot{\text{v}}\text{ = - sinθ-Dv}}^{\text{2}}$ and ${\text{v }\dot{\text{θ}}\text{ = - cosθ+v}}^{\text{2}}$. Investigate the case of positive drag.

Concept Introduction:

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

A conservative system does not posessany 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.