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Abstract
Noether’s theory of Birkhoff systems with unilateral constraints by introducing the quasi-symmetry of infinitesimal transformations of the transformation group Gr is presented and an example is given to illustrate the application of the result.

Keywords:
analytical mechanics/

Birkhoff systems with unilateral constraints/

conserved quantity/

symmetry/

Noether’s theorem
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ZHANG HONG-BIN

1.
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Cited By

[1]	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
[2]	Dong Wen-Shan, Huang Bao-Xin.Lie symmetries and Noether conserved quantities of generalized nonholonomic mechanical systems. Acta Physica Sinica, 2010, 59(1): 1-6.doi:10.7498/aps.59.1
[3]	Lou Zhi-Mei.The extended Prelle-Singer method for the conserved quantities of second-ordinary nonlinear coupled dynamics systems and their symmetries. Acta Physica Sinica, 2010, 59(2): 719-723.doi:10.7498/aps.59.719
[4]	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
[5]	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
[6]	Ge Wei-Kuan.Mei symmetry and conserved quantity of a holonomic system. Acta Physica Sinica, 2008, 57(11): 6714-6717.doi:10.7498/aps.57.6714
[7]	Luo Shao-Kai.A new type of non-Noether adiabatic invariants, i.e. adiabatic invariants of Lut zky type, for Lagrangian systems. Acta Physica Sinica, 2007, 56(10): 5580-5584.doi:10.7498/aps.56.5580
[8]	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
[9]	Zhang Yi.Non-Noether conserved quantities for systems with unilateral non-Chetaev nonholonomic constraints. Acta Physica Sinica, 2006, 55(2): 504-510.doi:10.7498/aps.55.504
[10]	Wu Hui-Bin, Mei Feng-Xiang.Symmetries of Lagrange system subjected to gyroscopic forces. Acta Physica Sinica, 2005, 54(6): 2474-2477.doi:10.7498/aps.54.2474
[11]	Xu Xue-Jun, Mei Feng-Xiang, Qin Mao-Chang.Hojman conserved quantity for a holonomic system in the event space. Acta Physica Sinica, 2005, 54(3): 1009-1014.doi:10.7498/aps.54.1009
[12]	Ge Wei-Kuan.Effects of mass variation on form invariance and conserved quantity of mechanical systems. Acta Physica Sinica, 2005, 54(6): 2478-2481.doi:10.7498/aps.54.2478
[13]	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
[14]	Zhang Yi.Symmetries and conserved quantities of mechanical systems with unilateral holonomic constraints in phase space. Acta Physica Sinica, 2005, 54(10): 4488-4495.doi:10.7498/aps.54.4488
[15]	Zhang Yi.Form invariance of mechanical systems with unilateral holonomic constraints. Acta Physica Sinica, 2004, 53(2): 331-336.doi:10.7498/aps.53.331
[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]	Zhang Yi.Effects of non-conservative forces and nonholonomic constraints on Lie symmetrie s of a Hamiltonian system. Acta Physica Sinica, 2003, 52(6): 1326-1331.doi:10.7498/aps.52.1326
[19]	Zhang Yi.. Acta Physica Sinica, 2002, 51(8): 1666-1670.doi:10.7498/aps.51.1666
[20]	Zhang Yi.. Acta Physica Sinica, 2002, 51(3): 461-464.doi:10.7498/aps.51.461

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Vol. 50, Issue 10 - 2001-05-20

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