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Chin. Phys., 2001, Vol. 10(4): 271-276    DOI: 10.1088/1009-1963/10/4/001
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BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM

Luo Shao-kai, Chen Xiang-wei, Fu Jing-li
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}×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:  Birkhoff's equation      geometrical description      global analysis      rotational relativistic system  
Received:  04 August 2000      Revised:  08 December 2000      Published:  11 July 2005
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, Chen Xiang-wei, Fu Jing-li BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM 2001 Chin. Phys. 10 271

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