Please wait a minute...
Chinese Physics, 2004, Vol. 13(12): 1999-2002    DOI: 10.1088/1009-1963/13/12/004
GENERAL Prev   Next  

Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system

Xu Xue-Jun (许学军)ab, Mei Feng-Xiang (梅凤翔)a, Qin Mao-Chang (秦茂昌)a
a Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract  Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relying on the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.
Keywords:  Birkhoffian system      form invariance      non-Noether conserved quantity  
Received:  11 May 2004      Revised:  03 June 2004      Accepted manuscript online: 
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  02.30.Hq (Ordinary differential equations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10272021).

Cite this article: 

Xu Xue-Jun (许学军), Mei Feng-Xiang (梅凤翔), Qin Mao-Chang (秦茂昌) Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system 2004 Chinese Physics 13 1999

[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] Conservation laws for Birkhoffian systems of Herglotz type
Yi Zhang(张毅), Xue Tian(田雪). Chin. Phys. B, 2018, 27(9): 090502.
[3] Generalized Birkhoffian representation of nonholonomic systems and its discrete variational algorithm
Shixing Liu(刘世兴), Chang Liu(刘畅), Wei Hua(花巍), Yongxin Guo(郭永新). Chin. Phys. B, 2016, 25(11): 114501.
[4] Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives
Lin-Li Wang (王琳莉) and Jing-Li Fu(傅景礼). Chin. Phys. B, 2016, 25(1): 014501.
[5] Bifurcation for the generalized Birkhoffian system
Mei Feng-Xiang (梅凤翔), Wu Hui-Bin (吴惠彬). Chin. Phys. B, 2015, 24(5): 054501.
[6] Skew-gradient representation of generalized Birkhoffian system
Mei Feng-Xiang (梅凤翔), Wu Hui-Bin (吴惠彬). Chin. Phys. B, 2015, 24(10): 104502.
[7] Noether's theorems of a fractional Birkhoffian system within Riemann–Liouville derivatives
Zhou Yan (周燕), Zhang Yi (张毅). Chin. Phys. B, 2014, 23(12): 124502.
[8] Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system
Jia Li-Qun(贾利群), Zhang Mei-Ling(张美玲), Wang Xiao-Xiao(王肖肖), and Han Yue-Lin(韩月林) . Chin. Phys. B, 2012, 21(7): 070204.
[9] 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.
[10] Type of integral and reduction for a generalized Birkhoffian system
Wu Hui-Bin(吴惠彬) and Mei Feng-Xiang(梅凤翔) . Chin. Phys. B, 2011, 20(10): 104501.
[11] Poisson theory and integration method of Birkhoffian systems in the event space
Zhang Yi(张毅). Chin. Phys. B, 2010, 19(8): 080301.
[12] Form invariance and new conserved quantity of generalised Birkhoffian system
Mei Feng-Xiang(梅凤翔) and Wu Hui-Bin(吴惠彬). Chin. Phys. B, 2010, 19(5): 050301.
[13] Symmetry and conserved quantities of discrete generalized Birkhoffian system
Zhang Ke-Jun(张克军), Fang Jian-Hui(方建会), and Li Yan(李燕). Chin. Phys. B, 2010, 19(12): 124601.
[14] 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.
[15] A potential integration method for Birkhoffian system
Hu Chu-Le(胡楚勒) and Xie Jia-Fang(解加芳). Chin. Phys. B, 2008, 17(4): 1153-1155.
No Suggested Reading articles found!