A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems

doi:10.1088/1009-1963/13/12/036

中国物理B ›› 2004, Vol. 13 ›› Issue (12): 2182-2186.doi: 10.1088/1009-1963/13/12/036

• • 上一篇

A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems

黄飞江¹, 卢一兵¹, 罗绍凯²

(1)Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China; (2)Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang University of Sciences, Hangzhou 310018, China; Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China

收稿日期:2004-03-02 修回日期:2004-08-23 出版日期:2004-12-17 发布日期:2005-03-17
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Hunan Province (Grant No 03JJY3005), and the Scientific Research Foundation of the Education Bureau of Hunan Province, China (Gran

A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems

Luo Shao-Kai (罗绍凯)^ab, Huang Fei-Jiang (黄飞江)^b, Lu Yi-Bing (卢一兵)^b

^a Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang University of Sciences, Hangzhou 310018, China; ^b Institute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, ChinaInstitute of Mathematical Mechanics and Mathematical Physics, Changsha University, Changsha 410003, China

Received:2004-03-02 Revised:2004-08-23 Online:2004-12-17 Published:2005-03-17
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10372053), the Natural Science Foundation of Hunan Province (Grant No 03JJY3005), and the Scientific Research Foundation of the Education Bureau of Hunan Province, China (Gran

摘要/Abstract

摘要： For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for t and q_s, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables t, q_s and \dot{q}_s. A series of deductions are inferred for a holonomic nonconservative system, Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.

关键词: nonholonomic system, Lie symmetry, non-Noether conserved quantity

Abstract: For a nonholonomic system, a new type of Lie symmetrical non-Noether conserved quantity is given under general infinitesimal transformations of groups in which time is variable. On the basis of the invariance theory of differential equations of motion under infinitesimal transformations for $t$ and $q_s$, we construct the Lie symmetrical determining equations, the constrained restriction equations and the additional restriction equations of the system. And a new type of Lie symmetrical non-Noether conserved quantity is directly obtained from the Lie symmetry of the system, which only depends on the variables $t$, $q_s$ and $\dot{q}_s$. A series of deductions are inferred for a holonomic nonconservative system, Lagrangian system and other dynamical systems in the case of vanishing of time variation. An example is given to illustrate the application of the results.

Key words: nonholonomic system, Lie symmetry, non-Noether conserved quantity

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

02.30.Hq (Ordinary differential equations)

罗绍凯, 黄飞江, 卢一兵. A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems[J]. 中国物理B, 2004, 13(12): 2182-2186.

Luo Shao-Kai (罗绍凯), Huang Fei-Jiang (黄飞江), Lu Yi-Bing (卢一兵). A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems[J]. Chinese Physics, 2004, 13(12): 2182-2186.

[1]	Hengchun Hu(胡恒春) and Yaqi Li(李雅琦). Lie symmetry analysis and invariant solutions for the (3+1)-dimensional Virasoro integrable model[J]. 中国物理B, 2023, 32(4): 40503-040503.
[2]	王勇, 崔金超, 陈菊, 郭永新. Quasi-canonicalization for linear homogeneous nonholonomic systems[J]. 中国物理B, 2020, 29(6): 64501-064501.
[3]	金世欣, 张毅. Generalized Chaplygin equations for nonholonomic systems on time scales[J]. 中国物理B, 2018, 27(2): 20502-020502.
[4]	刘世兴, 刘畅, 花巍, 郭永新. Generalized Birkhoffian representation of nonholonomic systems and its discrete variational algorithm[J]. 中国物理B, 2016, 25(11): 114501-114501.
[5]	王琳莉, 傅景礼. Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives[J]. 中国物理B, 2016, 25(1): 14501-014501.
[6]	孙毅, 陈本永, 傅景礼. Lie symmetry theorem of fractional nonholonomic systems[J]. , 2014, 23(11): 110201-110201.
[7]	陈爱永, 章丽娜, 温双全. Lie symmetries and exact solutions for a short-wave model[J]. 中国物理B, 2013, 22(4): 40510-040510.
[8]	赵纲领, 陈立群, 傅景礼, 洪方昱. Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices[J]. 中国物理B, 2013, 22(3): 30201-030201.
[9]	王肖肖, 韩月林, 张美玲, 贾利群. Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints[J]. 中国物理B, 2013, 22(2): 20201-020201.
[10]	贾利群, 张美玲, 王肖肖, 韩月林 . Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system[J]. 中国物理B, 2012, 21(7): 70204-070204.
[11]	方建会,张斌,张伟伟,徐瑞莉. Mei conserved quantity directly induced by Lie symmetry in a nonconservative Hamilton system[J]. 中国物理B, 2012, 21(5): 50202-050202.
[12]	刘晓巍, 李元成. Lie–Mei symmetry and conserved quantities of the Rosenberg problem[J]. 中国物理B, 2011, 20(7): 70204-070204.
[13]	姜文安, 李状君, 罗绍凯. Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems[J]. 中国物理B, 2011, 20(3): 30202-030202.
[14]	施沈阳, 傅景礼. Lie symmetry and Mei conservation law of continuum system[J]. 中国物理B, 2011, 20(2): 21101-021101.
[15]	张美玲, 孙现亭, 王肖肖, 解银丽, 贾利群. Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion[J]. 中国物理B, 2011, 20(11): 110202-110202.

A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems

A new type of Lie symmetrical non-Noether conserved quantity for nonholonomic systems

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