Chapter 5.P2, Problem 3P

In the following problem, we ask the reader to some of the details left out of the above discussion, to analyse the closed-loop system for the stability properties, and to conduct a numerical simulation of the nonlinear system.

Derive the linearized system (5) and (6).

$\varphi \text{'}\text{'}+2\delta \varphi \text{'}+{\omega }_0^2\varphi ={\alpha }_{0}y$ (5)

$Jy\text{'}=-\beta y+u,$ (6)