Wong's equations in Poisson geometry (Q2491047)

The author shows how Wong's equations of motion arise as the first order approximation of generic Hamiltonian systems on Poisson manifolds. The relation between Wong's equations and Hamiltonian systems are already been elucidated by Sternberg and Weinstein. In this paper, the author constructs for any symplectic leaf of a Poisson manifold a canonical Hamiltonian system and the corresponding linear approximation. He then obtains Wong's equations of motion. Finally, he shows how this result is related to Kaluza-Klein and gauge theory.