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