Chapter 6.6, Problem 4E

Interpretation Introduction

Interpretation:

For each of the reversible system ${\text{a) }\ddot{\text{x}}\text{ + (}\dot{\text{x}}\text{)}}^{\text{2}}{\text{ + x =3 b) }\dot{\text{x}}\text{ = y - y}}^{\text{3}}{\text{, }\dot{\text{y}}\text{ = x cosy c) }\dot{\text{x}}\text{ = siny, }\dot{\text{y}}\text{ = y}}^{\text{2}}\text{-x}$, sketch the phase portrait by hand and use a computer to check your sketch.

Concept Introduction:

Phase portrait is the geometrical representation of the trajectories of the dynamical system in the phase plane of the system equation. Each set of initial condition is represented by a different curve or a point in the phase plane.

A second-order system is said to be the time-reversal system if the time of the system is reversed, then the second-order derivative of the system is unchanged, and if the value of the first derivative is changed and the equation is unchanged, then the system is called as a time-reversal system.