Please wait a minute...
Chinese Physics, 2002, Vol. 11(5): 437-440    DOI: 10.1088/1009-1963/11/5/305
GENERAL Prev   Next  

Construction of the solution of variational equations for constrained Birkhoffian systems

Zhang Yi (张毅)
Department of Urban Construction, University of Science and Technology of Suzhou, Suzhou 215011, China
Abstract  In this paper we present the variational equations of constrained Birkhoffian systems and study their solution. It is proven that, under some conditions, a particular solution of variational equations can be obtained by using a first integral. At the end of the paper, an example is given to illustrate the application of the results.
Keywords:  analytical mechanics      constrained Birkhoffian system      variational equation      first integral  
Received:  27 October 2001      Revised:  26 December 2001      Accepted manuscript online: 
PACS:  02.30.Xx (Calculus of variations)  
  02.30.Rz (Integral equations)  
  02.30.Jr (Partial differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 19972010), and the "Qing Lan" Project Foundation of Jiangsu Province, China.

Cite this article: 

Zhang Yi (张毅) Construction of the solution of variational equations for constrained Birkhoffian systems 2002 Chinese Physics 11 437

[1] First integrals of the axisymmetric shape equation of lipid membranes
Yi-Heng Zhang(张一恒), Zachary McDargh, Zhan-Chun Tu(涂展春). Chin. Phys. B, 2018, 27(3): 038704.
[2] 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.
[3] 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.
[4] Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order
Feng Qing-Hua(冯青华), Meng Fan-Wei(孟凡伟), and Zhang Yao-Ming(张耀明) . Chin. Phys. B, 2011, 20(12): 120202.
[5] Applications of the first integral method to nonlinear evolution equations
Filiz Tacscan and Ahmet Bekir . Chin. Phys. B, 2010, 19(8): 080201.
[6] Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order
Deng Xi-Jun(邓习军), Yan Zi-Zong(燕子宗), and Han Li-Bo(韩立波). Chin. Phys. B, 2009, 18(8): 3169-3173.
[7] 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.
[8] Some new exact solutions to the Burgers--Fisher equation and generalized Burgers--Fisher equation
Jiang Lu(姜璐), Guo Yu-Cui(郭玉翠), and Xu Shu-Jiang(徐淑奖). Chin. Phys. B, 2007, 16(9): 2514-2522.
[9] Discrete variational principle and first integrals for Lagrange--Maxwell mechanico-electrical systems
Fu Jing-Li(傅景礼), Dai Gui-Dong(戴桂冬), Salvador Jimènez(萨尔瓦多·希梅尼斯), and Tang Yi-Fa(唐贻发). Chin. Phys. B, 2007, 16(3): 570-577.
[10] The discrete variational principle and the first integrals of Birkhoff systems
Zhang Hong-Bin(张宏彬), Chen Li-Qun(陈立群), Gu Shu-Long(顾书龙), and Liu Chuan-Zhang(柳传长). Chin. Phys. B, 2007, 16(3): 582-587.
[11] A Birkhoff-Noether method of solving differential equations
Shang Mei(尚玫), Guo Yong-Xin(郭永新), and Mei Feng-Xiang (梅凤翔). Chin. Phys. B, 2007, 16(2): 292-295.
[12] Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates
Lou Zhi-Mei (楼智美), Wang Wen-Long (汪文珑). Chin. Phys. B, 2006, 15(5): 895-898.
[13] Integrating factors and conservation theorems of constrained Birkhoffian systems
Qiao Yong-Fen(乔永芬), Zhao Shu-Hong(赵淑红), and Li Ren-Jie(李仁杰). Chin. Phys. B, 2006, 15(12): 2777-2781.
[14] The discrete variational principle in Hamiltonian formalism and first integrals
Zhang Hong-Bin (张宏彬), Chen Li-Qun (陈立群), Liu Rong-Wan (刘荣万). Chin. Phys. B, 2005, 14(6): 1063-1068.
[15] Discrete variational principle and the first integrals of the conservative holonomic systems in event space
Zhang Hong-Bin (张宏彬), Chen Li-Qun (陈礼群), Liu Rong-Wan (刘荣万). Chin. Phys. B, 2005, 14(5): 888-892.
No Suggested Reading articles found!