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On General Volume-Preserving Mechanical Systems via Cohomology |
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| Authors: | ZHOU Bin GUO Han-Ying WU Ke |
| Affiliation: | 1. Institute of High Energy Physics, the Chinese Academy of Sciences, P.O. Box 918-4, Beijing 100039, China;2. Institute of Theoretical Physics, the Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China;3. Department of Mathematics, Capital Normal University, Beijing 100037, China |
| Abstract: | We present the general form of equations that generate avolume-preserving flow on a symplectic manifold (M,ω) via the highest Euler-Lagrange cohomology. It is shownthat for every volume-preserving flow there are some 2-forms thatplay a similar role to the Hamiltonian in the Hamiltonmechanics and the ordinary canonical equations with Hamiltonian H are included as aspecial case with a 2-form Hω/(n-1). |
| Keywords: | volume-preserving mechanical system symplectic manifold cohomology |
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