Geodesic
Necessary conditions in the~inverse variational problem
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 285-288.

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In the paper the inverse variational problem in stratified speed spaces of arbitrary order is invariantly formulated, Lagrange cut is defined, and an analytic reformulation of the problem is given. We give a necessary condition of a system of ODE of even order not less than 4 to be a Lagrangian system. 
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     author = {Yu. F. Pastukhov},
     title = {Necessary conditions in the~inverse variational problem},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a18/}
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Yu. F. Pastukhov. Necessary conditions in the~inverse variational problem. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 285-288. http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a18/