An old Method of Jacobi to find Lagrangians

Details An old Method of Jacobi to find Lagrangians An old Method of Jacobi to find Lagrangians

2008-07-17

arxiv.org/abs/0807.2796v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages

Scientific paper

In a recent paper by Ibragimov [N. H. Ibragimov, Invariant Lagrangians and a new method of integration of nonlinear equations, J. Math. Anal. Appl. 304 (2005) 212--235] 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 to derive (many) Lagrangians of any second-order differential equation. The method is based on the search of the Jacobi Last Multipliers of the equations. We exemplify the simplicity and elegance of Jacobi's method by applying it to the same two equations as did Ibragimov. 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.

Affiliated with

Also associated with

No associations

Rating

An old Method of Jacobi to find Lagrangians does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An old Method of Jacobi to find Lagrangians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An old Method of Jacobi to find Lagrangians will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-42536