Please wait a minute...
Chin. Phys. B, 2008, Vol. 17(10): 3542-3548    DOI: 10.1088/1674-1056/17/10/003
GENERAL Prev   Next  

Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems

Luo Shao-Kai(罗绍凯)a)†, Cai Jian-Le(蔡建乐)b), and Jia Li-Qun(贾利群)c)
a  Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, ChinaDepartment of Physics, Hangzhou Teachers College, Hangzhou 310018, China; c School of Science,Southern Yangtze University, Wuxi 214122, China
Abstract  Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants,i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results.
Keywords:  analytical mechanics      disturbed holonomic nonconservative system      Lie symmetrical perturbation      adiabatic invariant of Lutzky type  
Received:  10 January 2008      Revised:  21 January 2008      Accepted manuscript online: 
PACS:  45.05.+x (General theory of classical mechanics of discrete systems)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10372053).

Cite this article: 

Luo Shao-Kai(罗绍凯), Cai Jian-Le(蔡建乐), and Jia Li-Qun(贾利群) Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems 2008 Chin. Phys. B 17 3542

[1] Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod
Wang Peng (王鹏), Xue Yun (薛纭), Liu Yu-Lu (刘宇陆). Chin. Phys. B, 2013, 22(10): 104503.
[2] Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics
Wang Peng(王鹏), Xue Yun(薛纭), and Liu Yu-Lu(刘宇陆) . Chin. Phys. B, 2012, 21(7): 070203.
[3] 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.
[4] Lie-form invariance of the Lagrange system
Wu Hui-Bin (吴惠彬). Chin. Phys. B, 2005, 14(3): 452-454.
[5] Methods of analytical mechanics for solving differential equations of first order
Wu Hui-Bin (吴惠彬), Mei Feng-Xiang (梅凤翔). Chin. Phys. B, 2005, 14(12): 2391-2394.
[6] Characteristic functional structure of infinitesimal symmetry transformations of Birkhoffian systems
Gu Shu-Long (顾书龙), Zhang Hong-Bin (张宏彬). Chin. Phys. B, 2004, 13(7): 979-983.
[7] A new conserved quantity of mechanical systems with differential constraints
Wu Hui-Bin (吴惠彬). Chin. Phys. B, 2004, 13(5): 589-591.
[8] Lie symmetries and invariants of constrained Hamiltonian systems
Liu Rong-Wan (刘荣万), Chen Li-Qun (陈立群). Chin. Phys. B, 2004, 13(10): 1615-1619.
[9] Lie symmetries and conserved quantities of Birkhoff systems with unilateral constraints
Zhang Hong-Bin (张宏彬), Gu Shu-Long (顾书龙). Chin. Phys. B, 2002, 11(8): 765-770.
[10] Construction of the solution of variational equations for constrained Birkhoffian systems
Zhang Yi (张毅). Chin. Phys. B, 2002, 11(5): 437-440.
[11] Noether's theorem of a rotational relativistic variable mass system
Fang Jian-Hui (方建会), Zhao Song-Qing (赵嵩卿). Chin. Phys. B, 2002, 11(5): 445-449.
[12] Study of the Lie symmetries of a relativistic variable mass system
Fang Jian-Hui (方建会). Chin. Phys. B, 2002, 11(4): 313-318.
[13] Form invariance and Lie symmetry of equations of non-holonomic systems
Wang Shu-Yong (王树勇), Mei Feng-Xiang (梅凤翔). Chin. Phys. B, 2002, 11(1): 5-8.
[14] NOETHER'S THEOREM OF NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS
Li Yuan-cheng (李元成), Zhang Yi (张毅), Liang Jing-hui (梁景辉), Mei Feng-xiang (梅凤翔). Chin. Phys. B, 2001, 10(5): 376-379.
[15] EFFECTS OF NON-CONSERVATIVE FORCES ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF A LAGRANGE SYSTEM
Zhang Rui-chao (张睿超), Chen Xiang-wei (陈向炜), Mei Feng-xiang (梅凤翔). Chin. Phys. B, 2000, 9(11): 801-804.
No Suggested Reading articles found!