Abstract
This Letter investigates the perturbation of symmetries and adiabatic invariants for the rotational relativistic Birkhoffian systems. The Pfaff–Birkhoff principle, equation of motion and equation of small disturbance are established. Lie symmetries, laws of conservations, symmetrical perturbations and adiabatic invariants are presented, based on the invariance of differential equations under infinitesimal transformations. The inverse problems are also discussed for the perturbation of the symmetries of these systems. The connection is demonstrated between the symmetrical perturbations of rotational relativistic Birkhoffian systems and those of classical rotational Birkhoffian systems. Finally, an example is discussed to further illustrate the applications.
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