Construction of Lagrangian and Hamiltonian Structures starting from one Constant of Motion

2014/01/23 by Sergio A. Hojman, Hojman, Sergio A.
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #physics.class-ph

paper · pdf · doi:10.48550/arxiv.1403.0557

6 pages, no figures

arxiv created 2014/01/23 · arxiv updated 2014/03/04

Abstract

The problem of the construction of Lagrangian and Hamiltonian structures starting from two first order equations of motion is presented. This new approach requires the knowledge of one (time independent) constant of motion for the dynamical system only. The Hamiltonian and Lagrangian structures are constructed, the Hamilton Jacobi equation is then written and solved and the second (time dependent) constant of the motion for the problem is explicitly exhibited.

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