An Old Method of Jacobi to Find Lagrangians
- https://doi.org/10.1142/S1402925109000467How to use a DOI?
- Lagrangian, Jacobi last multiplier, Lie symmetry, Noether symmetry
In a recent paper by Ibragimov a method was presented in order to find Lagrangians of certain second-order ordinary differential equations admitting a two-dimensional Lie symmetry algebra. We present a method devised by Jacobi which enables one to derive (many) Lagrangians of any second-order differential equation. The method is based on the search of the Jacobi Last Multipliers for the equations. We exemplify the simplicity and elegance of Jacobi's method by applying it to the same two equations as Ibragimov did. We show that the Lagrangians obtained by Ibragimov are particular cases of some of the many Lagrangians that can be obtained by Jacobi’s method.
- © 2009 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - M. C. Nucci AU - P. G. L. Leach PY - 2021 DA - 2021/01 TI - An Old Method of Jacobi to Find Lagrangians JO - Journal of Nonlinear Mathematical Physics SP - 431 EP - 441 VL - 16 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925109000467 DO - https://doi.org/10.1142/S1402925109000467 ID - Nucci2021 ER -