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A New Type of Non-Noether Adiabatic Invariants for Disturbed Lagrangian Systems: Adiabatic Invariants of Generalized Lutzky Type |
| LUO Shao-Kai |
| Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Ministry of Education), Zhejiang Sci-Tech University, Hangzhou 310018 |
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| Cite this article: |
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LUO Shao-Kai 2007 Chin. Phys. Lett. 24 2463-2466 |
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Abstract For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by
investigating the perturbation of Lie symmetries for a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results.
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02.20.Sv
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Received: 06 June 2007
Published: 16 August 2007
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| PACS: |
02.20.Sv
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(Lie algebras of Lie groups)
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