Chapter 8.7, Problem 5E

Interpretation Introduction

Interpretation:

By considering appropriate Poincare map, the system $\dot{\text{θ}}\text{ + sinθ = sint}$ has at least two periodic solutions is to be proven and the stability of the system is to be discussed.

Concept Introduction:

Poincare maps are used to study the flow near a periodic orbit.

Poincare map is defined by ${\text{x}}_{\text{k+1}}\text{ = P}\left({\text{x}}_{\text{k}}\right)$.