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Abstract
In this paper, the dynamics of Birkhoffian systems in the event space is studied. The Pfaff-Birkhoff-d'Alembert principle and Birkhoff's parametric equations for the Birkhoffian systems are established in the event space of (2n+1) dimensions. The first integrals of the parametric equations and the conditions for their existence are presented.

Keywords:
Birkhoffian system/

event space/

parametric equation/

first integral
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Zhang Yi

1.
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Cited By

[1]	Wang Yong, Mei Feng-Xiang, Cao Hui-Ying, Guo Yong-Xin.Improvement of field method and its application to integrating motion equation in Riemann-Cartan space. Acta Physica Sinica, 2018, 67(3): 034501.doi:10.7498/aps.67.20171583
[2]	Cui Jin-Chao, Liao Cui-Cui, Liu Shi-Xing, Mei Feng-Xiang.A method of judging a Birkhoffian to be a first integral of constrained mechanical system. Acta Physica Sinica, 2017, 66(4): 040201.doi:10.7498/aps.66.040201
[3]	Wu Hui-Bin, Mei Feng-Xiang.A gradient representation of holonomic system in the event space. Acta Physica Sinica, 2015, 64(23): 234501.doi:10.7498/aps.64.234501
[4]	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
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[6]	Jia Li-Qun, Cui Jin-Chao, Luo Shao-Kai, Zhang Yao-Yu.Mei symmetry and Mei conserved quantity of Nielsen equations for nonholonomic systems of unilateral non-Chetaev’s type in the event space. Acta Physica Sinica, 2009, 58(4): 2141-2146.doi:10.7498/aps.58.2141
[7]	Zhang Yi.Noether’s theory for Birkhoffian systems in the event space. Acta Physica Sinica, 2008, 57(5): 2643-2648.doi:10.7498/aps.57.2643
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[9]	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
[10]	Jia Li-Qun, Zheng Shi-Wang, Zhang Yao-Yu.Mei symmetry and Mei conserved quantity of nonholonomic systems of non-Chetaev’s type in event space. Acta Physica Sinica, 2007, 56(10): 5575-5579.doi:10.7498/aps.56.5575
[11]	Jia Li-Qun, Zhang Yao-Yu, Zheng Shi-Wang.Hojman conserved quantities for systems with non-Chetaev nonholonomic constraints in the event space. Acta Physica Sinica, 2007, 56(2): 649-654.doi:10.7498/aps.56.649
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Vol. 57, Issue 5 - 2008-03-05

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