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General Volume-Preserving Mechanical Systems
Authors:Zhou  Bin  Guo  Han-Ying  Wu   Ke
Affiliation:(1) Institute of High Energy Physics, Chinese Academy of Sciences, PO Box 918-4, Beijing, 100039, P.R. China;(2) Institute of Theoretical Physics, Chinese Academy of Sciences, PO Box 2735, Beijing, 100080, P.R. China;(3) Department of Mathematics, Capital Normal University, Beijing, 100037, P.R. China
Abstract:We present the general form of equations that generate a volume-preserving flow on a symplectic manifold M, ohgr) via the highest Euler–Lagrange cohomology. It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in Hamilton mechanics. The ordinary canonical equations are included as a special case with a 2-form 1/(n - 1)Hohgr, where H is the corresponding Hamiltonian.
Keywords:Euler–  Lagrange cohomology  symplectic  Hamiltonian  volume-preserving
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