General Volume-Preserving Mechanical Systems
Bin Zhou, Han-Ying Guo, Ke Wu
Abstract
In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, ω). 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 1n-1 H ωwhere H is the corresponding Hamiltonian.
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