Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems |
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Authors: | Luo Shao-Kai Cai Jian-Le and Jia Li-Qun |
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Institution: | Department of Physics, Hangzhou Teachers College,
Hangzhou 310018, China; Institute of Mathematical Mechanics and
Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou { rm
310018,
China; School of Science,Southern Yangtze University, Wuxi
214122, China |
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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. |
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Keywords: | analytical mechanics disturbed
holonomic nonconservative system Lie symmetrical perturbation adiabatic invariant of Lutzky type |
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