BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM

doi:10.1088/1009-1963/10/4/301

中国物理B ›› 2001, Vol. 10 ›› Issue (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

罗绍凯, 陈向炜, 傅景礼

Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, China

收稿日期:2000-08-04 修回日期:2000-12-08 出版日期:2001-04-15 发布日期:2005-07-11
基金资助:
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)

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

Received:2000-08-04 Revised:2000-12-08 Online:2001-04-15 Published:2005-07-11
Supported by:
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)

摘要/Abstract

摘要： 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.

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.

Key words: rotational relativistic system, Birkhoff's equation, geometrical description, global analysis

中图分类号: (Special relativity)

03.30.+p

02.40.Vh (Global analysis and analysis on manifolds)

罗绍凯, 陈向炜, 傅景礼. BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM[J]. 中国物理B, 2001, 10(4): 271-276.

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[J]. Chinese Physics, 2001, 10(4): 271-276.

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BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM

BIRKHOFF'S EQUATIONS AND GEOMETRICAL THEORY OF ROTATIONAL RELATIVISTIC SYSTEM

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