中国物理B ›› 2002, Vol. 11 ›› Issue (9): 859-863.doi: 10.1088/1009-1963/11/9/301

• GENERAL •    下一篇

Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems

乔永芬, 孟军, 赵淑红   

  1. Engineering College, Northeast Agricultural University, Harbin 150030, China
  • 收稿日期:2002-04-28 出版日期:2005-06-12 发布日期:2005-06-12

Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems

Qiao Yong-Fen (乔永芬), Meng Jun (孟军), Zhao Shu-Hong (赵淑红)   

  1. Engineering College, Northeast Agricultural University, Harbin 150030, China
  • Received:2002-04-28 Online:2005-06-12 Published:2005-06-12

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摘要： We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems. Firstly, we give the definition of integrating factors for the differential equations of motion of a mechanical system. Next, the necessary conditions for the existence of the conserved quantities are studied in detail. Then, we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system. Finally, an example is given to illustrate the application of the result.

Abstract: We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems. Firstly, we give the definition of integrating factors for the differential equations of motion of a mechanical system. Next, the necessary conditions for the existence of the conserved quantities are studied in detail. Then, we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system. Finally, an example is given to illustrate the application of the result.

Key words: nonholonomic system, relativity, integrating factor, conserved theorem

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq
03.30.+p (Special relativity)