Chapter 4.1, Problem 8E

Interpretation Introduction

Interpretation:

It is to be showed that the system $\dot{\text{θ}}\text{ = cosθ}$ has a single-valued potential $\text{V(θ)}$ and for $\dot{\text{θ}}\text{ = 1}$, there is no single valued potential $\text{V(θ)}$. The general rule is to be written. Also, it is to be determined when $\dot{\text{θ}}\text{ = f(θ)}$ would have a single valued potential.

Concept Introduction:

The function has single valued potential if its potential is $\text{2π}$ periodic, that is,

$\text{V}\left(\text{θ}\right)\text{ = V}\left(\text{θ + 2πk}\right)$ $\text{k}\in \text{z}$