Chapter 6.6, Problem 11E

Interpretation Introduction

Interpretation:

The rotational dynamics of an object in shear flow are governed by $\dot{\text{θ}}\text{ = cot}\left(\varphi \right)\text{ cosθ}$ and $\dot{\varphi }=\left({\cos }^2\left(\varphi \right)+A{\sin }^2\left(\varphi \right)\right)\text{ sinθ}$ shows that the equation in two ways under $\text{t }\to \text{ -t and θ }\to \text{ - θ}$ and under $\text{t }\to \text{ -t and }\varphi \to \text{ -}\varphi$. Investigate the phase portraits when A is positive, zero, and negative. Also, relate the result to the tumbling motion of an object in a shear flow.

Concept Introduction:

The geometrical representation of the trajectories of the dynamical system in the phase plane of the system equation is called a Phase potraite.

Every set of the initial condition is represented by a different curve or point in the phase plane.