A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

doi:10.1088/1009-1963/14/4/003

中国物理B ›› 2005, Vol. 14 ›› Issue (4): 656-659.doi: 10.1088/1009-1963/14/4/003

A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

蔡建乐¹, 罗绍凯², 贾利群³

(1)Department of Physics, Hangzhou Teachers College, Hangzhou,310018, China;; (2)Institute of Mathematical Mechanics and Mathematical Physics,Zhejiang Science-Technology University, Hangzhou, 310018, China; Institute of Mathematical Mechanics and Mathematical Physics,Changsha University, Changsha, 410003, China; Science College of Southern, Yangtze University, Wuxi,214063, China; (3)Science College of Southern, Yangtze University, Wuxi,214063, China

收稿日期:2004-06-21 修回日期:2004-12-15 出版日期:2005-04-20 发布日期:2005-03-28
基金资助:
Project supported by National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Hunan Province (Grant No 03JJY3005) and Scientific Research Foundation of Education Bureau of Hunan Province (Grant No 02C033).

A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

Luo Shao-Kai (罗绍凯)^abd, Cai Jian-Le (蔡建乐)^c, Jia Li-Qun (贾利群)^d

^a Institute of Mathematical Mechanics and Mathematical Physics,Zhejiang Science-Technology University, Hangzhou 310018, China; ^b Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003 China; ^c Department of Physics, Hangzhou Teachers College, Hangzhou 310018, China^d Science College of Southern, Yangtze University, Wuxi 214063, China

Received:2004-06-21 Revised:2004-12-15 Online:2005-04-20 Published:2005-03-28
Supported by:
Project supported by National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Hunan Province (Grant No 03JJY3005) and Scientific Research Foundation of Education Bureau of Hunan Province (Grant No 02C033).

摘要/Abstract

摘要： For the relativistic holonomic nonconservative system, a new Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the theory of invariance of differential equations of motion under infinitesimal transformations for $t$ and $q_s$, we construct the relativistic Lie symmetrical determining equations and obtain directly a new relativistic Lie symmetrical non-Noether conserved quantity of the system, which only depend on the variables $t$, $q_s$ and $\dot{q}_s$. An example is given to illustrate the application of the results.

Abstract: For the relativistic holonomic nonconservative system, a new Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the theory of invariance of differential equations of motion under infinitesimal transformations for $t$ and $q_s$, we construct the relativistic Lie symmetrical determining equations and obtain directly a new relativistic Lie symmetrical non-Noether conserved quantity of the system, which only depend on the variables $t$, $q_s$ and $\dot{q}_s$. An example is given to illustrate the application of the results.

Key words: relativity, holonomic nonconservative system, Lie symmetry, non-Noehter conserved quantity

中图分类号: (Special relativity)

03.30.+p

02.20.-a (Group theory) 45.05.+x (General theory of classical mechanics of discrete systems)

罗绍凯, 蔡建乐, 贾利群. A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations[J]. 中国物理B, 2005, 14(4): 656-659.

Luo Shao-Kai (罗绍凯), Cai Jian-Le (蔡建乐), Jia Li-Qun (贾利群). A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations[J]. Chinese Physics, 2005, 14(4): 656-659.

[1]	董国慧, 马宇翰, 陈劲夫, 王欣, 孙昌璞. Decoherence of macroscopic objects from relativistic effect[J]. 中国物理B, 2018, 27(10): 100301-100301.
[2]	王建武, 冯正和. Time-domain nature of group delay[J]. 中国物理B, 2015, 24(10): 100301-100301.
[3]	吴奇成, 文晶姬, 计新, Yeon Kyu-Hwang. Teleportation of three-dimensional single particle state in noninertial frames[J]. 中国物理B, 2014, 23(2): 20303-020303.
[4]	张启仁 . Relativity and impossibility of superluminal motion[J]. 中国物理B, 2012, 21(11): 110301-110301.
[5]	杨大宝, 李艳, 张福林, 陈景灵 . Demonstrating additional law of relativistic velocities based on squeezed light[J]. 中国物理B, 2012, 21(7): 74201-074201.
[6]	鲁重贤. Remarks on interpretations of the E?tv?s experiment and misinterpretation of E=mc²[J]. 中国物理B, 2007, 16(3): 635-639.
[7]	王智勇, 熊彩东. On the generator of Lorentz boost[J]. 中国物理B, 2006, 15(10): 2223-2227.
[8]	乔永芬, 赵淑红, 李仁杰. Form invariance and conserved quantities of Nielsen equations of relativistic variable mass nonholonomic systems[J]. 中国物理B, 2004, 13(3): 292-296.
[9]	方建会, 赵嵩卿. Noether's theorem of a rotational relativistic variable mass system[J]. 中国物理B, 2002, 11(5): 445-449.
[10]	乔永芬, 孟军, 赵淑红. Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems[J]. 中国物理B, 2002, 11(9): 859-863.
[11]	强稳朝. The calculating formula for radial matrix elements of a relativistic harmonic oscillator[J]. 中国物理B, 2003, 12(8): 831-835.
[12]	罗绍凯. Cyclic integrals and reduction of rotational relativistic Birkhoffian system[J]. 中国物理B, 2003, 12(2): 140-143.
[13]	马善钧, 刘明萍, 黄沛天. The forms of three-order Lagrangian equation in relative motion[J]. 中国物理B, 2005, 14(2): 244-246.
[14]	罗绍凯, 贾利群, 蔡建乐. A set of Lie symmetrical non-Noether conserved quantity for the relativistic Hamiltonian systems[J]. 中国物理B, 2003, 12(8): 841-845.
[15]	傅景礼, 陈立群, 骆毅, 罗绍凯. Stability for the equilibrium state manifold of relativistic Birkhoffian systems[J]. 中国物理B, 2003, 12(4): 351-356.

A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

A new non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0