Keywords: 
• 相对论性力学系统 /
• Birkhoff对称性 /
• 守恒量

Abstract: A new symmetry of a relativistic mechanical system is put forward, and the corresponding conserved quantity is given. The new symmetry is defined in such a way that if each solution to the differential equations of motion of a relativistic mechanical system corresponding to a set of Birkhoff's dynamical functions satisfies the differential equations of motion obtained by other set of Birkhoff's dynamical functions and vice versa, then the corresponding invariance is called a symmetry of Birkhoffians. We prove that the coefficient matrix which relates to the relativistic Birkhoff's equations obtained from two sets of Birkhoff's dynamical functions, is such that the trace of all its integer powers is a conserved quantity of the system, and therefore a theorem known for nonsingular equivalent Lagrangians presented by Currie and Saletan is extended to a relativistic Birkhoffian system. Two examples are given to illustrate the application of the results.