Birkhoff系统的Poincaré-Cartan积分不变量

基金项目: 国家自然科学基金资助项目(10175032);辽宁省自然科研基金资助项目(002083);河南省自然科学基金资助项目(998040080);辽宁省教育厅科研基金资助项目(990111004;20021004)

Poincaré-Cartan Integral Invariants of Birkhoffian Systems

1.
Department of Physics, Liaoning University, Shenyang 110036, China;
2.
Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China;
3.
Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 41

摘要: 基于现代微分几何学,分析了作为保守系统和非保守系统的推广——Birkhoff系统的辛结构.构造Birkhoff系统的Poincar-Cartan积分不变量.最后,将一维阻尼振动作为示例,求出其Poincar-Cartan积分不变量.
- Birkhoff系统 /
- 辛结构 /
- 自伴随 /
- Poincar-Cartan积分不变量
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 Poincar -Cartan's type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincar's type is found.
- Birkhoffian systems /
- symplectic structure /
- self-adjiontness /
- Poincar-Cartan integral invariants

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