Form Invariance and Noether Symmetries of Rotational Relativistic Birkhoff Systems**The project supported by National Natural Science Foundation of China under Grant No. 19972010, and Natural Science Foundation of Henan Province under Grant Nos. 984053100 and 998040080

Abstract

Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoff systems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic Pfaff-Birkhoff-D'Alembert principle under the infinitesimal transformations of groups, the theory of Noether symmetries of rotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noether symmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.