Integrating Factors and Conservation Laws for Relativistic Mechanical System

摘要

＜正＞ In this paper, we present a new method to construct the conservation laws for relativistic mechanicalsystems by finding corresponding integrating factors. First, the Lagrange equations or relativistic mechanical systemsare established, and the definition of integrating factors of thr systrms is given; second, the necessary conditions for theexistence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation betweentbe conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for thedetermination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems areestablished, and an example is given to illustrate the application of the results.