Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems
Luo Shao-Kai(罗绍凯)a)†, Cai Jian-Le(蔡建乐)b), and Jia Li-Qun(贾利群)c)
a Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Department of Physics, Hangzhou Teachers College, Hangzhou 310018, China;c School of Science，Southern Yangtze University, Wuxi 214122, China
Abstract Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants，i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results.
Received: 10 January 2008
Revised: 21 January 2008
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
Fund: Project supported by the National
Natural Science Foundation of China (Grant No
10372053).
Cite this article:
Luo Shao-Kai(罗绍凯), Cai Jian-Le(蔡建乐), and Jia Li-Qun(贾利群) Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems 2008 Chin. Phys. B 17 3542
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