Skew-gradient representation of generalized Birkhoffian system

doi:10.1088/1674-1056/24/10/104502

Abstract

The skew-gradient representation of a generalized Birkhoffian system is studied. A condition under which the generalized Birkhoffian system can be considered as a skew-gradient system is obtained. The properties of the skew-gradient system are used to study the properties, especially the stability, of the generalized Birkhoffian system. Some examples are given to illustrate the application of the result.

Keywords: generalized Birkhoffian system skew-gradient system Lyapunov function stability

Received: 28 February 2015
Revised: 15 May 2015
Accepted manuscript online:

PACS:	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	11.30.-j	(Symmetry and conservation laws)

Fund:

Project supported by the National Natural Science Foundation of China (Grant No. 11272050).

Corresponding Authors: Wu Hui-Bin
E-mail: huibinwu@bit.edu.cn

Cite this article:

Mei Feng-Xiang (梅凤翔), Wu Hui-Bin (吴惠彬) Skew-gradient representation of generalized Birkhoffian system 2015 Chin. Phys. B 24 104502

[1]	McLachlan R I, Quispel G R W and Robidoux N 1999 Phil. Tran. R. Soc. Lond. A 357 1021
[2]	Hirsch M W, Smale S and Devaney R L 2008 Differential Equations, Dynamical Systems, and an Introduction to Chaos(Singapore: Elsevier)
[3]	Quispel G R W and Capel H W 1996 Phys. Lett. A 218 223
[4]	Quispel G R W and Turner G S 1996 J. Phys. A: Math. Gen. 29 L341
[5]	Hong J L, Zhai S X and Zhang J J 2011 Siam J. Numer. Anal. 49 2017
[6]	Santilli R M 1983 Foundations of Theoretical MechanicsII (New York: Springer-Verlag)
[7]	Mei F X, Shi R C, Zhang Y F and Wu H B 1996 Dynamics of Birkhoffian System(Beijing: Beijing Institute of Technology Press) (in Chinese)
[8]	Galiullin A S, Gafarov G G, Malaishka R P and Khwan A M 1997 Analytical dynamics of Helmholtz, Birkhoff, Nambu systems(Moskow: UFN) (in Russian)
[9]	Chen X W 2002 Global Analysis of Birkhoff Systems(Kaifeng: Henan University Press) (in Chinese)
[10]	Zheng G H, Chen X W and Mei F X 2001 J. Beijing Institute of Technology 10 17
[11]	Guo Y X, Shang M and Luo S K 2003 Appl. Math. Mech. 24 76
[12]	Zhang Y 2002 Chin. Phys. 11 437
[13]	Xu X J, Mei F X and Qin M C 2004 Chin. Phys. 13 1999
[14]	Mei F X 1993 Sci. China Ser. A: Math. Phys. Astron. 36 1456
[15]	Mei F X and Wu H B 2012 J. Dynamics and Control 10 289 (in Chinese)
[16]	Mei F X 2013 Dynamics of Generalized Birkhoffian System(Beijing: Science Press) (in Chinese)

[1]	Modulational instability of a resonantly polariton condensate in discrete lattices Wei Qi(漆伟), Xiao-Gang Guo(郭晓刚), Liang-Wei Dong(董亮伟), and Xiao-Fei Zhang(张晓斐). Chin. Phys. B, 2023, 32(3): 030502.
[2]	Suppression of laser power error in a miniaturized atomic co-magnetometer based on split ratio optimization Wei-Jia Zhang(张伟佳), Wen-Feng Fan(范文峰), Shi-Miao Fan(范时秒), and Wei Quan(全伟). Chin. Phys. B, 2023, 32(3): 030701.
[3]	Continuous-wave optical enhancement cavity with 30-kW average power Xing Liu(柳兴), Xin-Yi Lu(陆心怡), Huan Wang(王焕), Li-Xin Yan(颜立新), Ren-Kai Li(李任恺), Wen-Hui Huang(黄文会), Chuan-Xiang Tang(唐传祥), Ronic Chiche, and Fabian Zomer. Chin. Phys. B, 2023, 32(3): 034206.
[4]	Improvement of coercivity thermal stability of sintered 2:17 SmCo permanent magnet by Nd doping Chao-Zhong Wang(王朝中), Lei Liu(刘雷), Ying-Li Sun(孙颖莉), Jiang-Tao Zhao(赵江涛), Bo Zhou (周波), Si-Si Tu(涂思思), Chun-Guo Wang(王春国), Yong Ding(丁勇), and A-Ru Yan(闫阿儒). Chin. Phys. B, 2023, 32(2): 020704.
[5]	Formation of nanobubbles generated by hydrate decomposition: A molecular dynamics study Zilin Wang(王梓霖), Liang Yang(杨亮), Changsheng Liu(刘长生), and Shiwei Lin(林仕伟). Chin. Phys. B, 2023, 32(2): 023101.
[6]	Formation of quaternary all-d-metal Heusler alloy by Co doping fcc type Ni₂MnV and mechanical grinding induced B2-fcc transformation Lu Peng(彭璐), Qiangqiang Zhang(张强强), Na Wang(王娜), Zhonghao Xia(夏中昊), Yajiu Zhang(张亚九),Zhigang Wu(吴志刚), Enke Liu(刘恩克), and Zhuhong Liu(柳祝红). Chin. Phys. B, 2023, 32(1): 017102.
[7]	Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[8]	Ion migration in metal halide perovskite QLEDs and its inhibition Yuhui Dong(董宇辉), Danni Yan(严丹妮), Shuai Yang(杨帅), Naiwei Wei(魏乃炜),Yousheng Zou(邹友生), and Haibo Zeng(曾海波). Chin. Phys. B, 2023, 32(1): 018507.
[9]	Parametric decay instabilities of lower hybrid waves on CFETR Taotao Zhou(周涛涛), Nong Xiang(项农), Chunyun Gan(甘春芸), Guozhang Jia(贾国章), and Jiale Chen(陈佳乐). Chin. Phys. B, 2022, 31(9): 095201.
[10]	Kinetic theory of Jeans' gravitational instability in millicharged dark matter system Hui Chen(陈辉), Wei-Heng Yang(杨伟恒), Yu-Zhen Xiong(熊玉珍), and San-Qiu Liu(刘三秋). Chin. Phys. B, 2022, 31(7): 070401.
[11]	Propagation and modulational instability of Rossby waves in stratified fluids Xiao-Qian Yang(杨晓倩), En-Gui Fan(范恩贵), and Ning Zhang(张宁). Chin. Phys. B, 2022, 31(7): 070202.
[12]	All polarization-maintaining Er:fiber-based optical frequency comb for frequency comparison of optical clocks Pan Zhang(张攀), Yan-Yan Zhang(张颜艳), Ming-Kun Li(李铭坤), Bing-Jie Rao(饶冰洁), Lu-Lu Yan(闫露露), Fa-Xi Chen(陈法喜), Xiao-Fei Zhang(张晓斐), Qun-Feng Chen(陈群峰), Hai-Feng Jiang(姜海峰)^‡, and Shou-Gang Zhang(张首刚). Chin. Phys. B, 2022, 31(5): 054210.
[13]	Stability and luminescence properties of CsPbBr₃/CdSe/Al core-shell quantum dots Heng Yao(姚恒), Anjiang Lu(陆安江), Zhongchen Bai(白忠臣), Jinguo Jiang(蒋劲国), and Shuijie Qin(秦水介). Chin. Phys. B, 2022, 31(4): 046106.
[14]	Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium: A stability analysis Astick Banerjee, Krishnendu Bhattacharyya, Sanat Kumar Mahato, and Ali J. Chamkha. Chin. Phys. B, 2022, 31(4): 044701.
[15]	Interrogation of optical Ramsey spectrum and stability study of an ⁸⁷Sr optical lattice clock Jing-Jing Xia(夏京京), Xiao-Tong Lu(卢晓同), and Hong Chang(常宏). Chin. Phys. B, 2022, 31(3): 034209.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Skew-gradient representation of generalized Birkhoffian system

Cite this article:

Online attention