中国物理B ›› 2006, Vol. 15 ›› Issue (9): 1935-1940.doi: 10.1088/1009-1963/15/9/006

• GENERAL • 上一篇    下一篇

A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics

张毅   

  1. Department of Civil Engineering, University of Science and Technology of Suzhou, Suzhou 215011, China
  • 收稿日期:2006-02-18 修回日期:2006-05-09 出版日期:2006-09-20 发布日期:2006-09-20
  • 基金资助:
    Project supported by the Natural Science Foundation of High Education of Jiangsu Province, China (Grant No 04KJA130135).

A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics

Zhang Yi(张毅)   

  1. Department of Civil Engineering, University of Science and Technology of Suzhou, Suzhou 215011, China
  • Received:2006-02-18 Revised:2006-05-09 Online:2006-09-20 Published:2006-09-20
  • Supported by:
    Project supported by the Natural Science Foundation of High Education of Jiangsu Province, China (Grant No 04KJA130135).

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摘要： The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics are studied. The exact invariant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invariant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invariant. An example is also given to illustrate the application of the results.

Abstract: The perturbations to symmetries and adiabatic invariants for nonconservative systems of generalized classical mechanics are studied. The exact invariant in the form of Hojman from a particular Lie symmetry for an undisturbed system of generalized mechanics is given. Based on the concept of high-order adiabatic invariant in generalized mechanics, the perturbation to Lie symmetry for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the nonconservative system of generalized classical mechanics is obtained, which can be called the Hojman adiabatic invariant. An example is also given to illustrate the application of the results.

Key words: generalized classical mechanics, adiabatic invariant, Lie symmetry, perturbation

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