中国物理B ›› 2000, Vol. 9 ›› Issue (10): 721-725.doi: 10.1088/1009-1963/9/10/001

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PERTURBATION TO THE SYMMETRIES AND ADIABATIC INVARIANTS OF HOLONOMIC VARIABLE MASS SYSTEMS

梅凤翔1, 陈向炜2   

  1. (1)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China
  • 收稿日期:2000-03-20 修回日期:2000-06-07 出版日期:2000-12-25 发布日期:2005-06-10
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 19972010), and by the Doctoral Program Foundation of Institution of Higher Education of China and by the Natural Science Foundation of Henan Province, China.

PERTURBATION TO THE SYMMETRIES AND ADIABATIC INVARIANTS OF HOLONOMIC VARIABLE MASS SYSTEMS

Chen Xiang-wei (梅凤翔)ab, Mei Feng-xiang (陈向炜)a   

  1. a Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China
  • Received:2000-03-20 Revised:2000-06-07 Online:2000-12-25 Published:2005-06-10
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 19972010), and by the Doctoral Program Foundation of Institution of Higher Education of China and by the Natural Science Foundation of Henan Province, China.

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摘要： The perturbation problem of symmetries for the holonomic variable mass systems under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then the corresponding inverse problem is studied. Finally an example is presented to illustrate these results.

Abstract: The perturbation problem of symmetries for the holonomic variable mass systems under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then the corresponding inverse problem is studied. Finally an example is presented to illustrate these results.

Key words: analytical mechanics, variable mass, symmetry, perturbation, adiabatic invariant

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.30.Zz (Inverse problems) 45.20.Jj (Lagrangian and Hamiltonian mechanics)