Geodesic
Seeking (and finding) Lagrangians
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 168-177

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It is well known that for any second-order ordinary differential equation (ODE), a Lagrangian always exists, and the key to its construction is the Jacobi last multiplier. Is it possible to find Lagrangians for first-order systems of ODEs or for higher-order ODEs? We show that the Jacobi last multiplier can also play a major role in this case.
Keywords: Lagrangian, first integral
Mots-clés : Jacobi last multiplier. 
@article{TMF_2009_160_1_a15,
     author = {M. C. Nucci},
     title = {Seeking (and finding) {Lagrangians}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {168--177},
     publisher = {mathdoc},
     volume = {160},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a15/}
}
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M. C. Nucci. Seeking (and finding) Lagrangians. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 168-177. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a15/