Derive the expression for the phase paths of the plane pendulum if the total energy is E

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Derive the expression for the phase paths of the plane pendulum if the total energy is E > 2mgl. Note that this is just the case of a particle moving in a periodic potential U (θ) = mgl (1 - cos θ).
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System Dynamics

ISBN: 978-0073398068

3rd edition

Authors: William Palm III

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