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Form invariance and noether symmetrical conserved quantity of relativistic Birkhoffian systems

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Abstract

A form invariance of the relativistic Birkhoffian system is studied, and the conserved quantities of the system are obtained. Under the infinitesimal transformation of groups, the definition and criteria of the form invariance of the system were given. In view of the invariance of relativistic Pfaff-Birkhoff-D' Alembert principle under the infinitesimal transformation of groups, the theory of Noethe, symmetries of the relativistic Birkhoffian system were constructed. The relation between the form invariance and the Noether symmetry is studied, and the results show that the form invariance can also lead to the Noether symmetrical conserved quantity of the relativistic Birkhoffian system under certain conditions.

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Authors and Affiliations

  1. Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, 410003, Changsha, P. R. China

    Luo Shao-kai

  2. Department of Applied Physics, Human University, 410082, Changsha, P.R.China

    Luo Shao-kai

  3. Science College, Southern Yangtze University, Wuxi, 214063, Jiangsu, P.R.China

    Luo Shao-kai

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  1. Luo Shao-kai
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Communicated by Lupin Zong-chi

Foundation items: the National Natural Science Foundation of China (19972010); the Natural Science Foundation of Henan Province (984053100, 998040080); the Scientific Research Foundation of the Education Bureau of Human Province (02C033)

Biography: Lupuo Shao-kai (1957−), Professor

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Shao-kai, L. Form invariance and noether symmetrical conserved quantity of relativistic Birkhoffian systems. Appl Math Mech 24, 468–478 (2003). https://doi.org/10.1007/BF02439627

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  • DOI: https://doi.org/10.1007/BF02439627

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