约束转动相对论性Birkhoff系统的几何理论

摘要

This paper focuses on studying the generalized geometry theory of constrained rotating relativistic Birkhoffian systems. Based on the fact that relativistic rotating inertia is embedded in the Birkhoffian systems, the Pfaff action of rotating relativistic Birkhoffian systems was defined. The Pfaff-Birkhoff principles and Birkhoff's equations of the constrained rotating relativistic systems were obtained. The geometrical description, the exact properties and their forms on R × T*M for the constrained rotating relativistic Birkhoffian systems are given. The global analyses of the autonomous, semi-autonomous and non-autonomous constrained relativistic Birkhoff's equations as well as the geometrical properties of energy change for the constrained rotating relativistic Birkhoffian systems were also conducted.