Europhys. Lett.
Volume 68, Number 4, November 2004
Page(s) 501 - 507
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 27 October 2004
Europhys. Lett., 68 (4), pp. 501-507 (2004)
DOI: 10.1209/epl/i2004-10247-9

On the transformation from Newtonian to Lagrangian description with Poisson bracket

S. K. Soni1 and Mukesh Kumar2

1  Department of Physics, SGTB Khalsa College, University of Delhi Delhi 110007, India
2  Department of Physics and Astrophysics, University of Delhi - Delhi 110007, India

received 16 February 2004; accepted in final form 29 September 2004
published online 27 October 2004

One of the most important problems in classical mechanics is how to transform from Newtonian to Lagrangian description. We propose to put this problem in the context of the Poisson bracket. Apart from suggesting a simple method for finding a transformation to a variational approach by systematic determination of a Lagrangian from Newton's equations of motion, the main result of this work is the demonstration of a new connection that the Poisson bracket expressed in terms of generalized coordinates and velocities has with the Helmholtz conditions. We comment also on the nonuniqueness of the Lagrangian.

45.20.-d - Formalisms in classical mechanics.
45.20.Jj - Lagrangian and Hamiltonian mechanics.

© EDP Sciences 2004