转动系统相对论性动力学方程的Birkhoff表示

给出转动力学系统的相对论性ＰｆａｆｆＢｉｒｋｈｏｆｆ 原理和Ｂｉｒｋｈｏｆｆ 方程．证明：相对论性完整保守转动力学系统可以直接纳入相对论性转动Ｂｉｒｋｈｏｆｆ 系统动力学；一般相对论性完整转动力学系统先将运动方程表成显形式，然后实行Ｂｉｒｋｈｏｆｆ 化．并给出应用实例．

BIRKHOFF REPRESENTATION OF RELATIVISTIC DYNAMICAL EQUATIONS OF ROTATIONAL CONSTRAINT MECHANICAL SYSTEMS

With the development of science and technology,more and more experiment facts were related to the problem of the high speed spinning.in 1985,M.carmele constructed the theory of rotational relativistic mechanics,and in recent years Luo Shaokai constructed the theory of the relativistic analytic mechanics for the rotational systems.Modern analytic mechanics emphasize on new mathematical methods.In this paper the Birkhoff's representation for relativistic rotational constraint mechanical systems are studied.The relativistic Pfaff action for rotational constraint mechanical systems are defined.The relativistic Pfaff Birkhoff principle and relativistic Birkhoff's equations for rotational mechanical systems are given.We lead through the relativistic generalized kinetic energy's function of the rotational systems.For the holonomic conservative mechanics systems,we can obtain relativistic Hamiltonian regular equations of the holonomic rotational systems,then which expressing directly as the form of the relativistic Birkhoff's equations for rotational systems.For the general holonomic relativistic rotational systems,the freezing derivatives and freezing partial derivative led through,the relativistic freezing derivative variation principle and the relativistic freezing derivative equations of dynamical for holonomic rotational systems and obtained,the relativistic freezing derivative equations of dynamical can be expressed the manifest form,then which are expressed as the form of Birkhoffian.At last an example is given.