转动系统的相对论性分析力学理论<sup>*</sup>

罗绍凯

转动系统的相对论性分析力学理论^*

罗绍凯

商丘师专, 河南商丘 476000

基金项目: * 河南省自然科学基金

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出版历程
- 收稿日期: 1996-10-24
- 修回日期: 1997-05-20
- 刊出日期: 1998-01-15

The Theory of Relativistic Analytical Mechanics of the Rotational Systems

Luo Shaokai

Shangqiu Teachers College, Shangqiu Henan 476000, P. R. China

摘要

摘要: 本文讨论了转动相对论力学理论,主要是建立转动系统的相对论性分析力学理论.构造转动系统的相对论性广义动能函数T_r^*= 和广义加速度能量函数S_r^*=,给出其Hamilton原理和三种不同形式的D'Alembert原理;对于完整约束系统,建立了转动系统的相对论性Lagrange方程、Nielsen方程、Appel方程和Hamilton正则方程;对于非完整约束系统,建立了转动系统的相对论性Routh方程、Чаплыгин方程、Nielsen方程和Appel方程;并给出转动系统的相对论性Noether守恒律.
- 转动系统 /
- 相对论 /
- 分析力学 /
- 非完整约束 /
- 变分原理 /
- 运动方程 /
- 守恒律
Abstract: The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics of the rotational systems is constructed. The relativistic generalized kinetic energy function for the rotational systems T_r^*= and the generalized acceleration energy function S_r^*= are constructed and further, the Hamilton 27 principle and three kinds of Dc Alembert principles are given. For the systems with holonomic constraints, the relativistic Lagrange equation, Nielsen equation, Appell equation and Hamilton canonical equation of the rotational systems are constructed; For the systems with nonholonomic constraints, the relativistic Routh equation, Chaplygin equation, Nielsen equation and Appell equation of the rotational systems are constructed; and the relativistic Noether conservation law of the rotational systems are given too
- rotational systems /
- relativity /
- analytical mechanics /
- nonholonomic constraints /
- variation principle /
- equation of motion /
- conservation law

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参考文献(16)

[1]	R.Bengtsson and S.Frauendorf,Quasiparticle spectra near the yrast line,Nucler Physics,A327(1979),139-171.
[2]	M.Carmeli,Field theory on R×S³ topology(Ⅰ~Ⅱ),Foundations of Physics,15(2)(1985),175-185.
[3]	M.Carmeli,The dynamics of rapidly rotating bodies,Foundations of Physics,15(8)(1985),889-903.
[4]	M.Carmeli,Field theory on R×S³ topology(Ⅲ),Foundations of Physics,15(10)(1985),1019-1029.
[5]	M.Carmeli,Rotational relativity theory,International Journal of Theoretical Physics,25(1)(1986),89-94.
[6]	罗绍凯,相对论性分析力学理论,教材通讯,(5)(1987),31-34.
[7]	罗绍凯,广义事件空间中的相对论性Hamilton原理和Lagrange方程,大学物理,11(10)(1992),14-16.
[8]	罗绍凯,相对论非线性非完整系统动力学理论,上海力学,12(1)(1991),67-70.
[9]	Luo Shaokai,Relativistic Variational principles and equations of motion of high-order nonlinear non-holonomic system,Proc.ICDVC,Peking University Press(1990),645-652.
[10]	罗绍凯,变质量任意阶非线性非完整系统的相对论性广义Volterra方程,数学物理学报,12(增刊)(1992),27-29.
[11]	罗绍凯,变质量可控力学系统的相对论性变分原理与运动方程,应用数学和力学,17(7)(1996),645-654.
[12]	梅凤翔,《非完整系统力学基础》,北京工业学院出版社(1985),81-311,316-357.
[13]	牛青萍,经典力学基本微分原理与不完整力学组的运动方程,力学学报,7(2)(1964),139-148.
[14]	罗绍凯,非完整非有势系统相对于非惯性系的广义Noether定理,应用数学和力学,12(9),(1991),863-872.
[15]	梅凤翔,《非完整动力学研究》,北京工业学院出版社(1987),181-275.
[16]	梅凤翔,《高等分析力学》,北京理工大学出版社(1991),392-529.