Hojman Conservation Laws for Relativistic Birkhoffian System**The project supported by National Natural Science Foundation of Chinaunder Grant No. 10272021

Abstract

For a relativistic Birkhoffian system, the Liesymmetry and Hojman conserved quantity are given under infinitesimaltransformations. On the basis of the invariance of relativistic Birkhoffianequations under infinitesimal transformations, Lie symmetricaltransformations of the system are constructed, which only depend on theBirkhoffian variables. The determining equations of Lie symmetry are given,and a Hojman conserved quantity is directly obtained from Lie symmetry ofthe system. An example is given to illustrate the application of the results.