Please wait a minute...
Chinese Physics, 2003, Vol. 12(12): 1349-1353    DOI: 10.1088/1009-1963/12/12/002
GENERAL Prev   Next  

Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

Chen Xiang-Wei (陈向炜), Li Yan-Min (李彦敏)
Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China
Abstract  Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results.
Keywords:  nonholonomic singular system      perturbation to symmetry      exact invariant      adiabatic invariant  
Received:  15 April 2003      Revised:  27 May 2003      Accepted manuscript online: 
PACS:  02.30.Zz (Inverse problems)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the Natural Science Foundation of Henan Province, China (Grant No 0311010900), and the Foundation of Young Key Member of the Teachers in Institutions of Higher Learning of Henan Province, China.

Cite this article: 

Chen Xiang-Wei (陈向炜), Li Yan-Min (李彦敏) Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system 2003 Chinese Physics 12 1349

[1] Conserved quantities and adiabatic invariants of fractional Birkhoffian system of Herglotz type
Juan-Juan Ding(丁娟娟), Yi Zhang(张毅). Chin. Phys. B, 2020, 29(4): 044501.
[2] Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems
Li-Li Xia(夏丽莉), Xin-Sheng Ge(戈新生), Li-Qun Chen(陈立群). Chin. Phys. B, 2019, 28(3): 030201.
[3] A new type of adiabatic invariants for disturbednon-conservative nonholonomic system
Xin-Xin Xu(徐鑫鑫), Yi Zhang(张毅). Chin. Phys. B, 2019, 28(12): 120402.
[4] Area and entropy spectra of black holes via an adiabatic invariant
Liu Cheng-Zhou(刘成周) . Chin. Phys. B, 2012, 21(7): 070401.
[5] Area spectrum of the three-dimensional Gödel black hole
Li Hui-Ling (李慧玲). Chin. Phys. B, 2012, 21(12): 120401.
[6] Perturbation to Mei symmetry and Mei adiabatic invariants for discrete generalized Birkhoffian system
Zhang Ke-Jun(张克军), Fang Jian-Hui(方建会), and Li Yan(李燕). Chin. Phys. B, 2011, 20(5): 054501.
[7] Perturbation of symmetries for super-long elastic slender rods
Ding Ning(丁宁) and Fang Jian-Hui(方建会) . Chin. Phys. B, 2011, 20(12): 120201.
[8] Perturbation to Mei symmetry and Mei adiabatic invariants for mechanical systems in phase space
Zhang Ming-Jiang(张明江), Fang Jian-Hui(方建会), Zhang Xiao-Ni(张小妮), and Lu Kai(路凯). Chin. Phys. B, 2008, 17(6): 1957-1961.
[9] Perturbation to Lie symmetry and another type of Hojman adiabatic invariants for Birkhoffian systems
Ding Ning(丁宁), Fang Jian-Hui(方建会), and Chen Xiang-Xia(陈相霞) . Chin. Phys. B, 2008, 17(6): 1967-1971.
[10] Perturbation to Mei symmetry and adiabatic invariants for Hamilton systems
Ding Ning(丁宁) and Fang Jian-Hui(方建会) . Chin. Phys. B, 2008, 17(5): 1550-1553.
[11] Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems
Luo Shao-Kai(罗绍凯), Cai Jian-Le(蔡建乐), and Jia Li-Qun(贾利群). Chin. Phys. B, 2008, 17(10): 3542-3548.
[12] 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). Chin. Phys. B, 2007, 16(6): 1516-1520.
[13] Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
Luo Shao-Kai(罗绍凯), Chen Xiang-Wei(陈向炜), and Guo Yong-Xin(郭永新). Chin. Phys. B, 2007, 16(11): 3176-3181.
[14] A new type of adiabatic invariants for nonconservative systems of generalized classical mechanics
Zhang Yi(张毅). Chin. Phys. B, 2006, 15(9): 1935-1940.
[15] Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations
Chen Xiang-Wei (陈向炜), Liu Cui-Mei (刘翠梅), Li Yan-Min (李彦敏). Chin. Phys. B, 2006, 15(3): 470-474.
No Suggested Reading articles found!