An Old Method of Jacobi to Find Lagrangians

被引：0

作者：

M. C. Nucci

P. G. L. Leach

机构：

[1] Università di Perugia,Dipartimento di Matematica e Informatica

[2] University of KwaZulu-Natal,School of Mathematical Sciences, Westville Campus

来源：

Journal of Nonlinear Mathematical Physics | 2009年 / 16卷

关键词：

Lagrangian; Jacobi last multiplier; Lie symmetry; Noether symmetry;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：431 / 441

页数：10

共 20 条

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