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Suppose that you have the Lagrangian L = 1 (;² + ở´n² ) + 420 for a 2D 20 system in plane polar coordinates (r, 0). Determine the Hamiltonian.

Suppose that you have the Lagrangian L = 1 (;² + ở´n² ) + 420 for a 2D 20 system in plane polar coordinates (r, 0). Determine the Hamiltonian.

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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.
Transcribed Image Text: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

Advanced Physics homework question answer, step 1, image 1

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

 

Conjugate momenta are given by

Advanced Physics homework question answer, step 1, image 2

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