Poincaré-cartan integral invariants of Birkhoffian systems |
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| Authors: | Guo Yong-xin Shang Mei Luo Shao-kai |
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| Affiliation: | (1) Department of Physics, Liaoning University, 110036 Shenyang, China;(2) Department of Applied Mechanics, Beijing Institute of Technology, 100081 Beijing, China;(3) Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, 410003 Changsha, China |
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| Abstract: | Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré-Cartan's type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré's type is found. Foundation items: the National Natural Science Foundation of China (10175032); the Natural Science Foundation of Liaoning Province of China (002083); the Natural Science Foundation of Henan Province of China (998040080); the Science Research Foundation of Liaoning Educational Committee of China (990111004, 20021004) Biography: GUO Yong-xin (1963-) Professor, Doctor E-mail: guoyongxin@hotmail.com |
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| Keywords: | Birkhoffian systems symplectic structure self-adjointness Poincaré-Cartan integral invariants |
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