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|
On the transformation from Newtonian to Lagrangian description with Poisson bracket
Department of Physics, SGTB Khalsa College, University of Delhi Delhi 110007, India
2 Department of Physics and Astrophysics, University of Delhi - Delhi 110007, India
Corresponding author: firstname.lastname@example.org
Accepted: 29 September 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.
PACS: 45.20.-d – Formalisms in classical mechanics / 45.20.Jj – Lagrangian and Hamiltonian mechanics
© EDP Sciences, 2004
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