It is to be showed that the system θ ˙ = cosθ has a single-valued potential V(θ) and for θ ˙ = 1 , there is no single valued potential V(θ) . The general rule is to be written. Also, it is to be determined when θ ˙ = f(θ) would have a single valued potential. Concept Introduction: The function has single valued potential if its potential is 2π periodic, that is, V ( θ ) = V ( θ + 2πk ) k ∈ z

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Chapter 4.1, Problem 8E

Interpretation Introduction

Interpretation:

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

Concept Introduction:

The function has single valued potential if its potential is 2π periodic, that is,

V(θ) = V(θ + 2πk) k∈z

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