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Abstract
Two new methods for the construction of the Birkhoffian representation of first-order systems are presented. The Birkhoffian functions Rμ and B can be computed from the differential equations. An example is given to illustrate the application of the methods.

Keywords:
analytical mechanics/

Birkhoff’s equation/

Birkhoffian representation/

first-order differential equation
Authors and contacts
Ding Guang-Tao
References

Cited By

[1]	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
[2]	Zhang Yi, Ge Wei-Kuan.An integral of a generalized Birkhoff system. Acta Physica Sinica, 2011, 60(5): 050202.doi:10.7498/aps.60.050202
[3]	Ding Guang-Tao.Hamiltonization of Whittaker equations. Acta Physica Sinica, 2010, 59(12): 8326-8329.doi:10.7498/aps.59.8326
[4]	Ding Guang-Tao.A study on the Lagrangian image of the Birkhoffian representations. Acta Physica Sinica, 2010, 59(1): 15-19.doi:10.7498/aps.59.15
[5]	Xue Yun, Weng De-Wei.Gauss principle for a super-thin elastic rod dynamics. Acta Physica Sinica, 2009, 58(1): 34-39.doi:10.7498/aps.58.34
[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]	Zhang Yi.Differential variational principles of mechanical systems in the event space. Acta Physica Sinica, 2007, 56(2): 655-660.doi:10.7498/aps.56.655
[9]	Hu Chu-Le, Xie Jia-Fang.Form invariance and Hojman conserved quantity of Maggi equation. Acta Physica Sinica, 2007, 56(9): 5045-5048.doi:10.7498/aps.56.5045
[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]	Mei Feng-Xiang, Xie Jia-Fang, Gang Tie-Qiang.Methods of analytical mechanics for integrating the Emden-Fowler equation. Acta Physica Sinica, 2007, 56(9): 5041-5044.doi:10.7498/aps.56.5041
[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]	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
[14]	Luo Shao-Kai, Mei Feng-Xiang.A non-Noether conserved quantity, i.e. Hojman conserved quantity, for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(3): 6-10.doi:10.7498/aps.53.6
[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]	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
[17]	Li Ren-Jie, Qiao Yong-Fen, Meng Jun.. Acta Physica Sinica, 2002, 51(1): 1-5.doi:10.7498/aps.51.1
[18]	Zhang Yi.. Acta Physica Sinica, 2002, 51(8): 1666-1670.doi:10.7498/aps.51.1666
[19]	Zhang Yi.. Acta Physica Sinica, 2002, 51(3): 461-464.doi:10.7498/aps.51.461
[20]	ZHANG HONG-BIN.NOETHER’S THEORY OF BIRKHOFF SYSTEMS WITH UNILATERAL CONSTRAINTS. Acta Physica Sinica, 2001, 50(10): 1837-1841.doi:10.7498/aps.50.1837

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Vol. 57, Issue 12 - 2008-06-20

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