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Hamiltonian and Lagrangian

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A system with one degree of freedom has a Hamiltonian

see attached

where A and B are certain functions of the coordinate q and p is the momentum conjugate to q.
a) Find the velocity q(dot)
b) Find the Lagrangian L(q q(dot)) (note variables)

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Solution Summary

The solution shows in detail how to convert a Hamiltonian to a Lagrangian.

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The Hamiltonian is:
(1.1)
Then, from Hamilton equation:
(1.2)
The Hamiltonian ...

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