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General Volume-Preserving Mechanical Systems |
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| Authors: | Zhou Bin Guo Han-Ying Wu Ke |
| Institution: | (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,  ) 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)H, where H is the corresponding Hamiltonian. |
| Keywords: | Euler– Lagrange cohomology symplectic Hamiltonian volume-preserving |
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