非完整系统相对于非惯性系的Noether理论

俞慧丹; 张解放; 许友生

非完整系统相对于非惯性系的Noether理论

浙江师范大学物理系金华

计量
- 文章访问数: 2251
- HTML全文浏览量: 146
- PDF下载量: 606
- 被引次数: 0
出版历程
- 收稿日期: 1992-04-02
- 刊出日期: 1993-06-15

Noether s Theory for Nonholonomic Dynamical Systems Relative to Noninertial Reference Frame

Physics Dept. of Zhejiang Normal University, Jinhua, Zhejiang

摘要

摘要: 本文通过构造广义惯性势,建立起非完整系统相对于非惯性系的新型Gauss型变分原理.提出并证明了非完整系统相对于非惯性系的Noether定理和逆定理.最后举例说明其应用.
- 广义势 /
- 非惯性参照系 /
- 非完整非有势系统 /
- Gauss型变分原理 /
- Noether定理 /
- Noether逆定理
Abstract: The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.
- generalized potential /
- non-inertial reference frame /
- nonholonomic nonpotential system /
- Gauss’s variational principle /
- Noether’s theorem /
- Noether’s inverse theorem

HTML全文

参考文献(18)

[1]	Noether,E.,Invariant variationsprobleme,Gottinger Nachyichten,Mathematish-Physicalishe Klasse 2(1918),235.
[2]	Courant,R.and D.Hilbert,Method of Mathematical Physics,Interscience Publishers.Inc.(1955),262.
[3]	Landau,L.D.and E.M.Lifshitz,The Classical Thoery of Fields,Pergamon Press(1975).
[4]	邹国兴.《量子场论导论》.科学出版社(1987).
[5]	Candotti,E.,C.Palmieri and B.Vitale,On the inversion of Noether's theorem in classical dynamical system,Am.J Phys.,40(1972),424-429.
[6]	Djukic,Dj.S.,Vujanovic,Noether's theory in classical nonconservative mechanics.Acta Mechanica,23(1975),17-27.
[7]	Vujanovic,B.,Conservation laws of dynamical systems via D'Alembert's principle,Int.J.Non-Linear Mech.,13(1978),185-197.
[8]	Salet,W.and F.Cantrijn,Generalization of Noether's theorem in classical mechanics,SIAM Review,23(1981),407-494.
[9]	李子平,约束系统的变换特点,物理学报,12(1981),1659-1673.
[10]	刘端,非完整非保守力学系统的守恒定律.力学学报,21(1989),76-83.
[11]	刘端,非完整非保守力学系统的Noether定理及逆定理,中国科学.A辑,(11)(1991),.1189-1195.
[12]	张解放.高阶非完整非保守力学系统的广义Nocther定理,科学通报.34(1989),1756-1757.
[13]	罗绍凯,非完整非有势力学系统相对于非惯比系灼广义Nocrher屯理和逆定理,应用数学和力学.12(9)(1931),863-870.
[14]	张解放.高阶非完整系统运动动力学,科学通报.23(1987),1836-1837.
[15]	Zhang Jie-fang,On the new forms of the motive differential equations of the mechanical system relative to non-inertial frame,Acta Mechanica Solida Sinica,4(1991),39-51.
[16]	朱青萍.经典力学的基本微分原理和非完整系统的运动方程,力学学报,7(2)(1964).
[17]	Novoselov,V.S.,Variational Methods in Mechanics,LGV(1966).(in Russian).
[18]	梅凤翔.有《非完整系统力学基础》,北京工业学院出版社(1985).