相对论性Birkhoff系统动力学方程的代数结构与Poisson积分方法

The Algebraic Structure and Poisson Integral Procedure of Dynamic Equation for Relativistic Birkhoof's Systems

定义相对论性Ｐｆａｆｆ作用量．得到相对论性Ｐｆａｆｆ－Ｂｉｒｋｈｏｆｆ原理和相对论性Ｂｉｒｋｈｏｆｆ方程．证明了自治形式和半自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程具有相容代数结构和Ｌｉｅ代数结构；一般非自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程没有代数结构．研究一种特殊的非自治形式的相对论性Ｂｉｒｋｈｏｆｆ方程，它具有相容代数结构和Ｌｉｅ容许代数结构．给出相对论性Ｂｉｒｋｈｏｆｆ方程的Ｐｏｉｓｓｏｎ积分方法．最后给出应用性实例．

Defining Pfaff action of relativistic systems, The Pfaff-Birkhoof principle and the Birkhoof's equation for relativistic systems are obtained. We prove that the au-tonomous Birkhoof equation of relativistic systems and the semi-autonomous Birkhoof's e-quation for relativistic systems have compatible algebraic structure and Lie's algebraic structure; and the non-autonomous Birkhoof's equation for the relativistic systems haven't algebraic structure in general. We study a special non-autonomous Birkhoof's equation for relativistic systems having compatible algebraic structure and Lie's admitted algebraic structure . The Poisson's integrals procedure of the Birkhoof's equation for relativistic systems are given. At last an example is given.