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Abstract
The Birkhoffian, the Birkhoff's functions, the Pfaff action, the Pfaff-Birkhoff principle and the Birkhoff equations of relativistic Birkhoff systems are given. The Birkhoff representation of relativistic dynamical systems is studied. Then the theory of Noether symmetries and Lie symmetries of the relativistic Birkhoff systems is obtained by the invariance of relativistic Pfaff action and relativistic Birkhoff equations under infinitesimal transformations. Finally the algebraic structure and Poisson integrals for the relativistic Birkhoff systems are studied.

Keywords:
relativity/

Birkhoff system/

noether symmetry/

Lie symmetry/

algebraic structure/

Poisson integral
Authors and contacts
FU JING-LI²,

CHEN LI-QUN²,

LUO SHAO-KAI¹,

CHEN XIANG-WEI¹,

WANG XIN-MIN¹
References

Cited By

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[2]	Xie Yin-Li, Jia Li-Qun, Yang Xin-Fang.Lie symmetry and Hojman conserved quantity of Nielsen equation in a dynamical system of the relative motion. Acta Physica Sinica, 2011, 60(3): 030201.doi:10.7498/aps.60.030201
[3]	Xia Li-Li, Li Yuan-Cheng.Non-Noether conserved quantity for relativistic nonholonomic controllable mechanical system with variable mass. Acta Physica Sinica, 2008, 57(8): 4652-4656.doi:10.7498/aps.57.4652
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[10]	Zhang Yi.Symmetries and Mei conserved quantities for systems of generalized classical mechanics. Acta Physica Sinica, 2005, 54(7): 2980-2984.doi:10.7498/aps.54.2980
[11]	Zhang Yi, Mei Feng-Xiang.Effects of constraints on Noether symmetries and conserved quantities in a Birkhoffian system. Acta Physica Sinica, 2004, 53(8): 2419-2423.doi:10.7498/aps.53.2419
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Vol. 50, Issue 12 - 2001-06-20

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