约束哈密顿系统在相空间中的精确不变量与绝热不变量

研究小干扰力作用下约束哈密顿系统对称性的摄动问题.建立了非保守约束哈密顿系统的正则方程,在增广相空间中研究了系统的对称性与精确不变量.基于力学系统的高阶绝热不变量的概念,给出了系统的各阶绝热不变量的形式及存在条件,并建立了绝热不变量与对称变换之间的对应关系 关键词： 约束哈密顿系统 对称性 摄动 不变量

Exact invariants and adiabatic invariants of constrained Hamiltonian systems in phase space

The perturbation problem of symmetries for constrained Hamiltonian systems under the action of small excitation is studied. Firstly, the canonical equations of nonconservative constrained Hamiltonian systems are established, and the symmetries and exact invariants of the systems in the extended phase space are studied. Secondly, according to the concept of high order adiabatic invariants of dynamical systems, this paper gives the form of adiabatic invariants and the conditions for their existence and establishes the relationship between adiabatic invariants and symmetrical transformations. Finally, an example is given to illustrate the application of the results.