A method for computing acceleration-dependent Lagrangians

Ding Guang-Tao

doi:10.7498/aps.58.6725

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
Authors and contacts
Ding Guang-Tao

1.
安徽师范大学物理与电子信息学院，芜湖 241000
References

Cited By

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[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
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[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
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[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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