Integration theory of the dynamics of a rotational relativistic system

The basic integration theory of the dynamics of a rotational relativistic s ystem is constructed. Firstly, the first integrals of the system are given. Secondly, the order of the equation of motion is reduced by using cyclic i ntegrals and energy integrals, and thus the generalized Routh equation and generalized Whittaker equation are obtained. Thirdly, the canonical equatio n and variational equation of the system are established, and the integral invariant is constructed by using the first integrals. Fourthly, the integr al variants and integral invariants of the Poincare-Cartan type are given. Finally, some deductions are given.