For any Lie algebroid with a regular Lagrangian, a family of Poisson brackets is built making the energy's Hamiltonian vector field a semispray.
Brahic,On the infinitesimal gauge symmetries of closed forms, J
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Hamiltonian semisprays on Lie algebroids
For any Lie algebroid with a regular Lagrangian, a family of Poisson brackets is built making the energy's Hamiltonian vector field a semispray.