Chapter 5.3, Problem 2E

Interpretation Introduction

Interpretation:

The romantic styles of Romeo and Juliet are to be characterized for the affair described by $\dot{\text{R}}\text{ = J, }\dot{\text{J}}\text{ = -R + J}$. Fixed points at the origin are to be classified, and its implication is to be written. Also, assuming $\text{ R(0) = 1, J(0) = 0,}$ $\text{ R(t) and J(t) are to be sketched}\text{.}$

Concept Introduction:

Love affairs represent the simple model to classify linear systems.

It is governed by a general linear system $\dot{\text{R}}\text{ = aR + bJ, }\dot{\text{J}}\text{ = cR + dJ}$ where a, b, c and d are parameters and their signs characterize the romantic styles of Romeo and Juliet.

$\text{ R(t) }$ represents Romeo’s love or hate for Juliet at time t, and $\text{ J(t) }$ represents Juliet’s love or hate for Romeo at time t.