Abstract:

This paper established the variational equations for relativistic Birk hoffian systems, and making use of the  Birkhoff equations  of the systems a nd their variational equations, the paper has proved that an integral invariant  can be directly constructed by a first integral of the systems. In the paper,two examples are given to illustrate the application of the results.

Key words: Relativity, Birkhoffian system, Variational equation, First integral; , Integral invariant