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Abstract
The purpose of this paper is to study the time-integral theorems for a generalized Birkhoff system. A time-integral identity of the system is presented. A power-like equation，a Virial-like theorem，an integral variational principle and a differential variational principle for the system are deduced by using the time-integral identity.

Keywords:
generalized Birkhoff system/

time-integral theorem/

power-like equation/

variational principle
Authors and contacts
Ge Wei-Kuan²,

Mei Feng-Xiang¹
References

Cited By

[1]	Li Yan-Min, Chen Xiang-Wei, Wu Hui-Bin, Mei Feng-Xiang.Two kinds of generalized gradient representations for generalized Birkhoff system. Acta Physica Sinica, 2016, 65(8): 080201.doi:10.7498/aps.65.080201
[2]	Mei Feng-Xiang, Wu Hui-Bin.Generalized Birkhoff system and a kind of combined gradient system. Acta Physica Sinica, 2015, 64(18): 184501.doi:10.7498/aps.64.184501
[3]	Zou Dan-Dan, Yang Wei-Hong.Dynamically accessible variations for two-fluid plasma model. Acta Physica Sinica, 2014, 63(3): 030401.doi:10.7498/aps.63.030401
[4]	Zhang Xin-You, L. J. Li, Huang Y. C..Euler-Lagrange equation for general n-order character functional and unification of quantitative causal principle, principle of relativity and general Newton’s laws. Acta Physica Sinica, 2014, 63(19): 190301.doi:10.7498/aps.63.190301
[5]	Xue Yun, Weng De-Wei, Chen Li-Qun.Methods of analytical mechanics for exact Cosserat elastic rod dynamics. Acta Physica Sinica, 2013, 62(4): 044601.doi:10.7498/aps.62.044601
[6]	Ge Wei-Kuan, Zhang Yi, Lou Zhi-Mei.Infinitesimal canonical transformation and integral for a generalized Birkhoff system. Acta Physica Sinica, 2012, 61(14): 140204.doi:10.7498/aps.61.140204
[7]	Zhang Yi, Ge Wei-Kuan.An integral of a generalized Birkhoff system. Acta Physica Sinica, 2011, 60(5): 050202.doi:10.7498/aps.60.050202
[8]	Zhou Xian-Chun, Lin Wan-Tao, Lin Yi-Hua, Yao Jing-Sun, Mo Jia-Qi.A method of solving a class of disturbed Lorenz system. Acta Physica Sinica, 2011, 60(11): 110207.doi:10.7498/aps.60.110207
[9]	Wu Zhao-Chun.Variational principle and its boundary and additional boundary conditions for inverse shape design problem of heat conduction. Acta Physica Sinica, 2010, 59(9): 6326-6330.doi:10.7498/aps.59.6326
[10]	Zhang Yi.Stability of equilibrium for the autonomous generalized Birkhoffian system. Acta Physica Sinica, 2010, 59(1): 20-24.doi:10.7498/aps.59.20
[11]	Li Yan-Min, Mei Feng-Xiang.Generalized canonical transformations of a kind of generalized Birkhoff systems. Acta Physica Sinica, 2010, 59(8): 5219-5222.doi:10.7498/aps.59.5219
[12]	Wang Chuan-Dong, Liu Shi-Xing, Mei Feng-Xiang.Generalized Pfaff-Birkhoff-d’Alembert principle and form invariance of generalized Birkhoff’s equations. Acta Physica Sinica, 2010, 59(12): 8322-8325.doi:10.7498/aps.59.8322
[13]	Li Yan-Min, Mei Feng-Xiang.Integral methods for the generalized Birkhoff equations. Acta Physica Sinica, 2010, 59(9): 5930-5933.doi:10.7498/aps.59.5930
[14]	Zhang Yi.Birkhoff symmetries and conserved quantities of generalized Birkhoffian systems. Acta Physica Sinica, 2009, 58(11): 7436-7439.doi:10.7498/aps.58.7436
[15]	Mei Feng-Xiang, Xie Jia-Fang, Gang Tie-Qiang.An inverse problem of dynamics of a generalized Birkhoff system. Acta Physica Sinica, 2008, 57(8): 4649-4651.doi:10.7498/aps.57.4649
[16]	Ge Wei_Kuan, Mei Feng_Xiang.Time-integral theorems for Birkhoff systems. Acta Physica Sinica, 2007, 56(5): 2479-2481.doi:10.7498/aps.56.2479
[17]	Xue Yun, Liu Yan-Zhu, Chen Li-Qun.Methods of analytical mechanics for dynamics of the Kirchhoff elastic rod. Acta Physica Sinica, 2006, 55(8): 3845-3851.doi:10.7498/aps.55.3845
[18]	Huang Yong-Chang, Li Xi-Guo.Unification of different integral variational principles. Acta Physica Sinica, 2005, 54(8): 3473-3479.doi:10.7498/aps.54.3473
[19]	Jiang Jin-Huan, Li Zi-Ping.Interaction potential between spatial optical solitons based on holographic focusing mechanism. Acta Physica Sinica, 2004, 53(9): 2991-2994.doi:10.7498/aps.53.2991
[20]	LUO SHAO-KAI, FU JING-LI, CHEN XIANG-WEI.BASIC THEORY OF RELATIVISTIC BIRKHOFFIAN DYNAMICS OF ROTATIONAL SYSTEM. Acta Physica Sinica, 2001, 50(3): 383-389.doi:10.7498/aps.50.383

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Vol. 58, Issue 2 - 2009-01-20

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