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Generalized geometric Hamilton-Jacobi theorem on Lie algebroids
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In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi theorem for Hamiltonian system on Lie algebroids. Then this results are generalized and two types of time-dependent Hamilton-Jacobi theorem of Hamiltonian system on Lie algebroids are obtained.
Forward citations
Cited by 2 Pith papers
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Optimal control problems on the co-adjoint Lie groupoids
Any right-invariant optimal control problem on a Lie groupoid is claimed to reduce to one on its co-adjoint Lie algebroid, but the key step is cited, not proven.
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A note on integrabiliy of Hamiltonian systems on the co-adjoint Lie groupoids
On co-adjoint Lie groupoids of product form, Hamiltonian integrability is claimed to reduce to the integrability of a Hamiltonian system on a co-adjoint orbit, but the derivation is not sound.
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