Birkhoff's equations and geometrical theory of rotational relativistic system

The Birkhoffian and Birkhoff's functions of a rotational relativistic syste m are constructed, the Pfaff action of rotational relativistic system is de fined, the Pfaff-Birkhoff principle of a rotational relativistic system is given, and the Pfaff-Birkhoff-D'Alembert principles and Birkhoff's equation s of rotational relativistic system are constructed. The geometrical descri ption of a rotational relativistic system is studied, and the exact propert ies of Birkhoff's equations and their forms on (R) over right arrow x T*M f or a rotational relativistic system are obtained. The global analysis of Bi rkhoff's equations for a rotational relativistic system is studied, the glo bal properties of autonomous, semi-autonomous and non-autonomous rotational relativistic Birkhoff's equations, and the geometrical properties of energ y change for rotational relativistic Birkhoff's equations are given.