转动相对论系统的Lie对称性和守恒量

傅景礼; 陈向炜; 罗绍凯

转动相对论系统的Lie对称性和守恒量

商丘师范学院数学力学与数学物理研究所, 河南商丘 476000

基金项目: 国家自然科学基金(19972010);河南省自然科学基金资助课题(934060800,984053100)

详细信息

作者简介:
傅景礼(1955~ ),男,副教授,研究方向:一般力学,发表论文30余篇.

中图分类号: O316;O410
计量
- 文章访问数: 2892
- HTML全文浏览量: 186
- PDF下载量: 720
- 被引次数: 0
出版历程
- 收稿日期: 1998-08-06
- 修回日期: 2000-01-01
- 刊出日期: 2000-05-15

Lie Symmetries and Conserved Quantities of Rotational Relativistic Systems

Research Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu, Henan 476000, P. R. China

摘要

摘要: 研究转动相对论性完整与非完整力学系统的Lie对称性和守恒量.定义转动相对论力学系统的无限小变换生成元,利用微分方程在无限小变换下的不变性,建立转动相对论性力学系统的Lie对称确定方程,得到结构方程和守恒量的形式,并给出应用实例.
- 转动系统 /
- 相对论 /
- 分析力学 /
- Lie对称 /
- 守恒量 /
- 微分方程
Abstract: The Lie symmetries and conserved quantities of the rotational relativistic holonomic and nonholonomic systems were studied. By defining the infinitesimal transformations' generators and by using the invariance of the differential equations under the infinitesimal transformations, the determining equations of Lie symmetries for the rotational ralativistic mechanical systems are established. The structure equations and the forms of conserved quantities are obtained. An example to illustrate the application of the results is given.
- rotational systems /
- relativity /
- analytic mechanics /
- Lie symmetry /
- conserved quantity /
- differential equation

HTML全文

参考文献(15)

[1]	Bengtsson R,Frauendorf S.Quasiparticle spectr a near the yrast line[J].Nucler Physics,1979,A327:139～171.
[2]	罗绍凯.相对论性分析力学理论[J].教材通迅,1987,(5):31～34.
[3]	罗绍凯.相对论非线性非完整系统动力学理论[J].上海力学,1991,12(1):67～70.
[4]	Luo Shaokai.Relativistic variational principles and equations of motion high-order nonlinear nonholonomic system[A].In:Proc ICDVC[C].Beijing:Peking University Press,1990,645～652.
[5]	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[J].应用数学和力学,1996,17(7):645～654.
[6]	Carmeli M.Field theory on R×S³ topology (Ⅰ～Ⅱ)[J].Foundations of Physics,1985,15(2):175～185.
[7]	Carmeli M.The dynamics of rapidly rotating bodies[J].Foundations of Physics,1985,15(8):889～903.
[8]	Carmeli M.Field theory on R×S³ topology (Ⅲ)[J].Foundations of Physics,1985,15(10):1019～1029.
[9]	Carmeli M.Rotational relativity theory[J].International Journal of Theoretical Physics,1986,25(1):89～94.
[10]	罗绍凯.转动系统的相对论性分析力学理论[J].应用数学和力学,1998,19(1):43～53.
[11]	李子平.经典和量子约束系统及其对称性质[M].北京:北京工业大学出版社,1993,244～351.
[12]	梅凤翔.Birkhoff系统的Noether理论[J].中国科学(A辑),1993,23(7):709～717.
[13]	梅凤翔.李群和李代数对约束力学系统的某些应用[A].见:现代数学和力学(MMM-Ⅶ)[C].上海:上海大学出版社,1997,32～40.
[14]	Lutzky M.Dynamical symmetries and conserved quantities[J].J Phy A Math,1979,12(7):973～981.
[15]	赵跃宇,梅凤翔.关于力学系统的对称性与不变量[J].力学进展,1993,23(3):360～372