FORM INVARIANCE AND NOETHER SYMMETRICAL CONSERVED QUANTITY OF RELATIVISTIC BIRKHOFFIAN SYSTEMS

Abstract

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 Noether 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.

2010 MSC Number:

LUO Shao-kai. FORM INVARIANCE AND NOETHER SYMMETRICAL CONSERVED QUANTITY OF RELATIVISTIC BIRKHOFFIAN SYSTEMS. Applied Mathematics and Mechanics (English Edition), 2003, 24(4): 468-478.

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