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Suppose that you have the Lagrangian

\[ L = \frac{21}{20} \left( \dot{r}^2 + \dot{\theta}^2 r^2 \right) + \frac{420}{r} \]

for a 2D system in plane polar coordinates \((r, \theta)\).

Determine the Hamiltonian.

Expert Solution

Concept

Hamiltonian of the system is given by

Where L = Lagrangian of the system, p_q = Conjugate momenta corresponding to canonical variable q

Conjugate momenta are given by

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