Abstract
In this paper, we have studied the positive problems of perturbation to the symmetries for relativistic Birkhoffian systems under the action of a small force of the disturbance. The fundamental theory, equations of motion and equation of small disturbance of relativistic Birkhoffian systems were established. Lie symmetries and conserved quantity of this systems were given. Perturbation to the symmetries of the systems under infinitesimal transformations, s-order adiabatic invariants, existence conditions and the form of adiabatic invariants were studied. We have also studied the inverse problems of perturbation to the symmetries for relativistic Birkhoffian systems. We obtain the perturbation to the symmetries of the systems under infinitesimal transformations, when the systems possess s-order adiabatic invariants. The relationship between relativistic Birkhoffian systems and classical Birkhoffian systems were studied. Finally an example was presented to illustrate the result.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
