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Abstract
This paper studies the geometric foundations of Hojman theorem for Brikhoffian s y stems. The differential equations of motion and the Hojman conservation law of t he systems are established. A proof of Hojman theorem of Birkhoffian systems is given by use of the modern differential geometry.

Keywords:
Birkhoffian system/

Hojman theorem/

symmetry/

differential geometry
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Zhang Yi

1.
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Cited By

[1]	Zhang Yi.Mei’s symmetry theorems for non-migrated Birkhoffian systems on a time scale. Acta Physica Sinica, 2021, 70(24): 244501.doi:10.7498/aps.70.20210372
[2]	Chen Ju, Zhang Yi.Perturbation to Noether symmetries and adiabatic invariants for Birkhoffian systems based on El-Nabulsi dynamical models. Acta Physica Sinica, 2014, 63(10): 104501.doi:10.7498/aps.63.104501
[3]	Cui Jin-Chao, Zhao Zhe, Guo Yong-Xin.General Hojman's method for the construction of Birkhoffian representation. Acta Physica Sinica, 2013, 62(9): 090205.doi:10.7498/aps.62.090205
[4]	Tan Ping-An, Yang Lei, Zhang Bo.Spatio-temporal synchronization of parameter mismatch system based on differential geometry theory. Acta Physica Sinica, 2013, 62(23): 230507.doi:10.7498/aps.62.230507
[5]	Ding Guang-Tao.Hojman method for construction of Birkhoffian representation and the Birkhoff symmetry. Acta Physica Sinica, 2010, 59(6): 3643-3647.doi:10.7498/aps.59.3643
[6]	Lu Kai, Fang Jian-Hui, Zhang Ming-Jiang, Wang Peng.Noether symmetry and Mei symmetry of discrete holonomic system in phase space. Acta Physica Sinica, 2009, 58(11): 7421-7425.doi:10.7498/aps.58.7421
[7]	Ding Guang-Tao.Effects of gauge transformations on symmetries of Birkhoffian system. Acta Physica Sinica, 2009, 58(11): 7431-7435.doi:10.7498/aps.58.7431
[8]	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
[9]	Jing Hong-Xing, Li Yuan-Cheng, Xia Li-Li.Perturbation of Lie symmetries and a type of generalized Hojman adiabatic invariants for variable mass systems with unilateral holonomic constraints. Acta Physica Sinica, 2007, 56(6): 3043-3049.doi:10.7498/aps.56.3043
[10]	Hu Chu-Le.Lie symmetries and Hojman conserved quantities of one kind of differential equations of motion of nonholonomic systems. Acta Physica Sinica, 2007, 56(7): 3675-3677.doi:10.7498/aps.56.3675
[11]	Zhang Peng-Yu, Fang Jian-Hui.Lie symmetry and non-Noether conserved quantities of variable mass Birkhoffian system. Acta Physica Sinica, 2006, 55(8): 3813-3816.doi:10.7498/aps.55.3813
[12]	Wu Hui-Bin, Zhang Yong-Fa, Mei Feng-Xiang.Hojman method for solving differential equations. Acta Physica Sinica, 2006, 55(10): 4987-4990.doi:10.7498/aps.55.4987
[13]	Zhang Yi, Fan Cun-Xin, Mei Feng-Xiang.Perturbation of symmetries and Hojman adiabatic invariants for Lagrangian system. Acta Physica Sinica, 2006, 55(7): 3237-3240.doi:10.7498/aps.55.3237
[14]	Zheng Shi-Wang, Fu Jing-Li, Li Xian-Hui.Momentum-dependent symmetries and non-Noether conserved quantities for mechanico-electrical systems. Acta Physica Sinica, 2005, 54(12): 5511-5516.doi:10.7498/aps.54.5511
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[16]	Luo Shao-Kai.Mei symmetry,Noether symmetry and Lie symmetry of Hamiltonian canonical equations in a singular system. Acta Physica Sinica, 2004, 53(1): 5-10.doi:10.7498/aps.53.5
[17]	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
[18]	Qiao Yong-Fen, Zhao Shu-Hong, Li Ren-Jie.Non Noether conserved quantity of the holonomic mechanical systems in terms of quasi-coordinates ——An extension of Hojman theorem. Acta Physica Sinica, 2004, 53(7): 2035-2039.doi:10.7498/aps.53.2035
[19]	Zhang Yi.. Acta Physica Sinica, 2002, 51(3): 461-464.doi:10.7498/aps.51.461
[20]	Zhang Yi.. Acta Physica Sinica, 2002, 51(8): 1666-1670.doi:10.7498/aps.51.1666

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Vol. 53, Issue 12 - 2004-06-20

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