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The Lagrangian for a symmetric top, in terms of Euler angles $\theta,\phi,\psi$ is given by $$ L = {1\over2} I_1 \left(\dot{\theta}^2 + \dot{\phi}^2 \sin^2\theta \right) +{1\over2} I_3 (\dot{\psi} + \dot{\phi} \cos\theta)^2 - mgL\cos\theta $$
- Compute the canonical momenta conjugate to $\theta,\phi,\psi.$
- Show that the Hamiltonian in terms of momenta $p_\theta, p_\phi$ and $p_\psi$ the Euler angles is given by $$H=\frac{p_\theta^2}{2I_1} + \frac{(p_\psi -p_\phi \cos\theta)^2}{2 I_1 \sin^2\theta} + \frac{p_\psi^2}{2I_3} + mgL\cos\theta$$
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4727:Diamond Point
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