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Abstract
Symmetry theory of the generalized Hamilton-Tabarrok-Leech’s canonical equations is presented. The differential equations of motion of systems are written. The Noether symmetry, the form invariance and the Lie symmetry of systems are studied, and the corresponding conserved quantities are found. Finally, an example is given to illustrate the application of the results.

Keywords:
generalized classical mechanics/

H-T-L canonical equation/

symmetry/

conserved quantity
Authors and contacts
Qiao Yong-Fen¹,

Zhao Shu-Hong¹,

Li Ren-Jie²
References

Cited By

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[2]	Lou Zhi-Mei, Mei Feng-Xiang.The third independent conserved quantity and its symmetry of the two-dimensional anisotropic harmonic oscillator. Acta Physica Sinica, 2012, 61(11): 110201.doi:10.7498/aps.61.110201
[3]	Li Yuan-Cheng, Xia Li-Li, Wang Xiao-Ming, Liu Xiao-Wei.Lie-Mei symmetry and conserved quantities of Appell equation for a holonomic mechanical system. Acta Physica Sinica, 2010, 59(6): 3639-3642.doi:10.7498/aps.59.3639
[4]	Li Yuan-Cheng, Wang Xiao-Ming, Xia Li-Li.Unified symmetry and conserved quantities of Nielsen equation for a holonomic mechanical system. Acta Physica Sinica, 2010, 59(5): 2935-2938.doi:10.7498/aps.59.2935
[5]	Zhang Yi, Xue Yun, Ge Wei-Kuan.Symmetries and conserved quantities of the Rosenberg problem. Acta Physica Sinica, 2010, 59(7): 4434-4436.doi:10.7498/aps.59.4434
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[7]	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
[8]	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
[9]	Jia Li-Qun, Cui Jin-Chao, Zhang Yao-Yu, Luo Shao-Kai.Lie symmetry and conserved quantity of Appell equation for a Chetaev’s type constrained mechanical system. Acta Physica Sinica, 2009, 58(1): 16-21.doi:10.7498/aps.58.16
[10]	Zheng Shi-Wang, Jia Li-Qun.Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems. Acta Physica Sinica, 2007, 56(2): 661-665.doi:10.7498/aps.56.661
[11]	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
[12]	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
[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]	Lou Zhi-Mei.Parametric orbit equation and symmetries of classical particle in the field of noncentral force. Acta Physica Sinica, 2005, 54(4): 1460-1463.doi:10.7498/aps.54.1460
[16]	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
[17]	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
[18]	Mei Feng-Xiang.Lie symmetry and the conserved quantity of a generalized Hamiltonian system. Acta Physica Sinica, 2003, 52(5): 1048-1050.doi:10.7498/aps.52.1048
[19]	Zhang Yi.A conservation theorem of Hojman for systems of generalized classical mechanics. Acta Physica Sinica, 2003, 52(8): 1832-1836.doi:10.7498/aps.52.1832
[20]	Zhang Yi.. Acta Physica Sinica, 2002, 51(3): 461-464.doi:10.7498/aps.51.461

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Vol. 55, Issue 11 - 2006-06-05

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