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Chinese Physics, 2001, Vol. 10(4): 271-276    DOI: 10.1088/1009-1963/10/4/301
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BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM

Luo Shao-kai (罗绍凯), Chen Xiang-wei (陈向炜), Fu Jing-li (傅景礼)
Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, China
Abstract  The Birkhoffian and Birkhoff's functions of a rotational relativistic system are constructed, the Pfaff action of rotational relativistic system is defined, the Pfaff-Birkhoff principle of a rotational relativistic system is given, and the Pfaff-Birkhoff-D'Alembert principles and Birkhoff's equations of rotational relativistic system are constructed. The geometrical description of a rotational relativistic system is studied, and the exact properties of Birkhoff's equations and their forms on $\vec{R}\times T*M$ for a rotational relativistic system are obtained. The global analysis of Birkhoff's equations for a rotational relativistic system is studied, the global properties of autonomous, semi-autonomous and non-autonomous rotational relativistic Birkhoff's equations, and the geometrical properties of energy change for rotational relativistic Birkhoff's equations are given.
Keywords:  rotational relativistic system      Birkhoff's equation      geometrical description      global analysis  
Received:  04 August 2000      Revised:  08 December 2000      Accepted manuscript online: 
PACS:  03.30.+p (Special relativity)  
  02.40.Vh (Global analysis and analysis on manifolds)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 19972010) and the Natural Science Foundation of Henan Province (Grant Nos. 984053100, 998040080, 934060800)

Cite this article: 

Luo Shao-kai (罗绍凯), Chen Xiang-wei (陈向炜), Fu Jing-li (傅景礼) BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM 2001 Chinese Physics 10 271

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