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Abstract
The problem of constructing an acceleration-dependent Lagrangian from the equations of motion is studied. A method for the computation of an acceleration-dependent Lagrangian from the self-adjoint equations is presented. Two examples are given to illustrate the application of the results.

Keywords:
analytical mechanics/

acceleration-dependent Lagrangian/

self-adjointness/

inverse problem of Lagrangian mechanics
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Ding Guang-Tao

1.
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Cited By

[1]	Ding Guang-Tao.Acceleration-dependent Lagrangians in classical mechanics. Acta Physica Sinica, 2009, 58(6): 3620-3624.doi:10.7498/aps.58.3620
[2]	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
[3]	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
[4]	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
[5]	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
[6]	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
[7]	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
[8]	Zhang Yi.Lutzky conserved quantities and velocity-dependent symmetries for systems with unilateral holonomic constraints. Acta Physica Sinica, 2006, 55(5): 2109-2114.doi:10.7498/aps.55.2109
[9]	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
[10]	Mei Feng-Xiang, Xu Xue-Jun.Reduction of generalized Chaplygin systems. Acta Physica Sinica, 2005, 54(9): 3975-3977.doi:10.7498/aps.54.3975
[11]	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
[12]	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
[13]	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
[14]	Luo Shao-Kai, Guo Yong-Xin, Mei Feng-Xiang.Noether symmetry and Hojman conserved quantity for nonholonomic mechanical systems. Acta Physica Sinica, 2004, 53(5): 1270-1275.doi:10.7498/aps.53.1270
[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 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
[17]	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
[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]	FANG JIAN-HUI.CONSERVATION LAWS OF RELATIVISTIC VARIABLE MASS SYSTEMS. Acta Physica Sinica, 2001, 50(6): 1001-1005.doi:10.7498/aps.50.1001

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Vol. 58, Issue 10 - 2009-05-20

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