 Hamiltonian flow preserves a constant-level Lagrangian (source code)

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= Hamiltonian flow preserves a constant-level Lagrangian

If a Hamiltonian is constant on a Lagrangian $L$, then $dH$ vanishes on $TL$. Hence its Hamiltonian vector field belongs to $(TL)^\omega=TL$, and its flow preserves $L$.

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