中国物理B ›› 2007, Vol. 16 ›› Issue (11): 3182-3186.doi: 10.1088/1009-1963/16/11/006

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Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

罗绍凯   

  1. Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China;Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Zhejiang Sci-Tech University), Ministry of Education, Hangzhou
  • 出版日期:2007-11-20 发布日期:2007-11-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10372053 and 10472040).

Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

Luo Shao-Kai(罗绍凯)a)b)†   

  1. a Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Zhejiang Sci-Tech University), Ministry of Education, Hangzhou 310018, China
  • Online:2007-11-20 Published:2007-11-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10372053 and 10472040).

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摘要： For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables $t$, $q_s $ and $\dot {q}_s $. An example is given to illustrate the application of the results.

关键词: relativity, holonomic nonconservative system, Noether symmetry, non-Noether conserved quantity

Abstract: For a relativistic holonomic nonconservative system, by using the Noether symmetry, a new non-Noether conserved quantity is given under general infinitesimal transformations of groups. On the basis of the theory of invariance of differential equations of motion under general infinitesimal transformations, we construct the relativistic Noether symmetry, Lie symmetry and the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations. By using the Noether symmetry, a new relativistic non-Noether conserved quantity is given which only depends on the variables $t$, $q_s $ and $\dot{q}_s $. An example is given to illustrate the application of the results.

Key words: relativity, holonomic nonconservative system, Noether symmetry, non-Noether conserved quantity

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj