Abstract
Routh order reduction method of the relativistic Birkhoffianequations is studied. For a relativistic Birkhoffian system, the cyclicintegrals can be found by using the perfect differential method.Through these cyclic integrals, the order of the system can be reduced.If the relativistic Birkhoffian system has a cyclic integral, then theBirkhoffian equations can be reduced at least by two degrees and theBirkhoffian form can be kept. The relations among the relativisticBirkhoffian mechanics, the relativistic Hamiltonian mechanics, and therelativistic Lagrangian mechanics are discussed, and the Routh orderreduction method of the relativistic Lagrangian system is obtained.And an example is given to illustrate the application of the result.
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