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物理学报. 2007, 56(10): 5580-5584.
doi: 10.7498/aps.56.5580.
Lagrange系统一类新型的非Noether绝热不变量——Lutzky型绝热不变量
- 收稿日期: 2007-05-17
- 修回日期: 2007-06-02
- 刊出日期: 2007-05-05
摘要: 研究了Lagrange系统的Lie对称性摄动与新型的非Noether绝热不变量. 列出了未受扰Lagrange系统的Lie对称性导致的Lutzky型精确不变量；基于力学系统的高阶绝热不变量的定义，研究在小扰动作用下Lagrange系统Lie对称性的摄动，得到了系统的一类Lutzky形式的绝热不变量.举例说明方法和结果的应用.
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关键词:
- 分析力学 /
- Lagrange系统 /
- 对称性 /
- 摄动
English Abstract
A new type of non-Noether adiabatic invariants, i.e. adiabatic invariants of Lut zky type, for Lagrangian systems
- Received Date:
17 May 2007
- Accepted Date:
02 June 2007
- Published Online:
05 May 2007
Abstract: The perturbation of Lie symmetries and new non-Noether adiabatic invariants for the Lagrangian system are studied. The exact invariants of Lutzky type arising f rom the Lie symmetries of Lagrangian system without perturbation are given. Base d on the definition of high-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for Lagrangian system under the action of smal l disturbances is investigated, and a type of Lutzky adiabatic invariants of the system are obtained. An example is given to illustrate the application of the m ethod and results.
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Keywords:
- analytical mechanics /
- Lagrangian system /
- symmetry /
- perturbation
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