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I'm trying to find

1. The Hamiltonian

2. The Hamilton equation of motion for the flyball governor shown in problem 2 here

http://www.srl.caltech.edu/phys106/1999/Homework3.pdf

This is what i have. Can someone tell me if i'm right?

[tex]

\begin{gather*}

L = ml^2\dot{\theta}^2+ ml^2\omega^2\sin^2\theta + 2Ml^2\dot{\theta}^2\sin^2\theta +2(m+M)gl\cos\theta\\

H = ml^2\dot{\theta}^2+ ml^2\omega^2\sin^2\theta + 2Ml^2\dot{\theta}^2\sin^2\theta -2(m+M)gl\cos\theta\\

\partial{L}/\partial\dot{\theta} = 2ml^2\dot{\theta} + 4Ml^2\dot{\theta}\sin^2\theta = P_\theta\\

\dot{\theta} =P_\theta/2ml^2\dot{\theta} + 4Ml^2\dot{\theta}\sin^2\theta\\

\partial{H}/\partial{P_\theta} = P_\theta/2ml^2\dot{\theta} + 4Ml^2\dot{\theta}\sin^2\theta = \dot{\theta}\\

\partial{H}/\partial\theta = 2ml^2\omega^2\sin\theta\cos\theta +4Ml^2\dot{\theta}^2\sin\theta\cos\theta + 2(m+M)gl\sin\theta = -\dot{P_\theta}\\

-\dot{P_\theta}=-(ml^2\ddot{\theta}+4Ml^2\ddot{\theta}\sin^2\theta

\\

equating the two equations and solving for theta double dot, we get\\

\ddot{\theta} = \frac{ml\omega^2\sin\theta\cos\theta+2Ml\dot{\theta}^2\sin\theta\cos\theta-(m+M)g\sin\theta}{l(m+2M\sin^2\theta)}\\

\end{gather*} [/tex]

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# Homework Help: Hamiltonian of flyball governor

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