Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical  systems with non-Chetaev type constraints

doi:10.1088/1009-1963/16/6/004

中国物理B ›› 2007, Vol. 16 ›› Issue (6): 1516-1520.doi: 10.1088/1009-1963/16/6/004

Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints

夏丽莉, 李元成

College of Physics Science and Technology, China University of Petroleum Dongying 257061, China

收稿日期:2006-09-21 修回日期:2006-10-11 出版日期:2007-06-20 发布日期:2007-06-20
基金资助:
Project supported by the Graduate Students' Innovative Foundation of China University of Petroleum (East China) (Grant No~S2006-31).

Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints

Xia Li-Li(夏丽莉)^† and Li Yuan-Cheng(李元成）

College of Physics Science and Technology, China University of Petroleum Dongying 257061, China

Received:2006-09-21 Revised:2006-10-11 Online:2007-06-20 Published:2007-06-20
Supported by:
Project supported by the Graduate Students' Innovative Foundation of China University of Petroleum (East China) (Grant No~S2006-31).

摘要/Abstract

摘要： This paper studies the perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints. It gives the exact invariants introduced by the Lie symmetries of the nonholonomic controllable mechanical system with non-Chetaev type constraints without perturbation. Based on the definition of high-order adiabatic invariants of mechanical system, the perturbation of Lie symmetries for nonholonomic controllable mechanical system with non-Chetaev type constraints with the action of small disturbances is investigated, and a new type of adiabatic invariant of system are obtained. In the end of this paper, an example is given to illustrate the application of the results.

Abstract: This paper studies the perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints. It gives the exact invariants introduced by the Lie symmetries of the nonholonomic controllable mechanical system with non-Chetaev type constraints without perturbation. Based on the definition of high-order adiabatic invariants of mechanical system, the perturbation of Lie symmetries for nonholonomic controllable mechanical system with non-Chetaev type constraints with the action of small disturbances is investigated, and a new type of adiabatic invariant of system are obtained. In the end of this paper, an example is given to illustrate the application of the results.

Key words: nonholonomic controllable mechanical system, symmetry, perturbation, adiabatic invariant

中图分类号: (General properties, structure, and representation of Lie groups)

02.20.Qs

02.30.-f (Function theory, analysis)

夏丽莉, 李元成. Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints[J]. 中国物理B, 2007, 16(6): 1516-1520.

Xia Li-Li(夏丽莉) and Li Yuan-Cheng(李元成）. Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints[J]. Chinese Physics, 2007, 16(6): 1516-1520.

[1]	夏丽莉, 陈立群, 傅景礼, 吴旌贺. Symmetries and variational calculationof discrete Hamiltonian systems[J]. , 2014, 23(7): 70201-070201.
[2]	夏丽莉, 陈立群. Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices[J]. 中国物理B, 2012, 21(7): 70202-070202.
[3]	李燕, 方建会, 张克军. Conformal invariance and a kind of Hojman conserved quantity of the Nambu system[J]. 中国物理B, 2011, 20(3): 30201-030201.
[4]	李佑宁, 黄华俊. Nonlinear dynamical symmetries of Smorodinsky–Winternitz and and Fokas–Lagerstorm systems[J]. 中国物理B, 2011, 20(1): 10302-010302.
[5]	刘希忠. Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method[J]. 中国物理B, 2010, 19(8): 80202-080202.
[6]	赵丽, 傅景礼, 陈本永. Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration[J]. 中国物理B, 2010, 19(1): 10301-010301.
[7]	张毅. Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space[J]. 中国物理B, 2009, 18(11): 4636-4642.
[8]	李元成, 夏丽莉, 王小明. Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems[J]. 中国物理B, 2009, 18(11): 4643-4649.
[9]	张明江, 方建会, 路凯, 张克军, 李燕. Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems[J]. 中国物理B, 2009, 18(11): 4650-4656.
[10]	夏丽莉, 蔡建乐, 李元成. Conformal invariance and conserved quantities of general holonomic systems in phase space[J]. 中国物理B, 2009, 18(8): 3158-3162.
[11]	张智勇, 雍雪林, 陈玉福. A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations[J]. 中国物理B, 2009, 18(7): 2629-2633.
[12]	傅景礼, 聂宁明, 黄健飞, Jimé nez Salvador, 唐贻发, Vá zquez Luis, 赵维加. Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices[J]. 中国物理B, 2009, 18(7): 2634-2641.
[13]	崔金超, 张耀宇, 贾利群. Mei conserved quantity of Nielsen equation for anon-Chetaev-type non-holonomic system[J]. 中国物理B, 2009, 18(5): 1731-1736.
[14]	傅景礼, 陈本永, 谢凤萍. Noether symmetries of discrete mechanico-electrical systems[J]. 中国物理B, 2008, 17(12): 4354-4360.
[15]	蔺鹏, 方建会, 庞婷. Lie symmetry and Hojman conserved quantity of Nambu system[J]. 中国物理B, 2008, 17(12): 4361-4364.

Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints

Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints

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