General Volume-Preserving Mechanical Systems

Details General Volume-Preserving Mechanical Systems General Volume-Preserving Mechanical Systems

2002-08-23

arxiv.org/abs/math-ph/0208033v1

Physics

Mathematical Physics

Plain LaTeX, 13 pages, no figures

Scientific paper

In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, \omega). It is shown that every volume-preserving flow has some 2-forms acting the role of the Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton equations are included as a special case with a 2-form \frac{1}{n-1} H \omega where H is the corresponding Hamiltonian.

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