Geodesic
On the equivalence of variational problems. II
Archivum mathematicum, Tome 29 (1993) no. 3-4, pp. 197-220
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Elements of general theory of infinitely prolonged underdetermined systems of ordinary differential equations are outlined and applied to the equivalence of one-dimensional constrained variational integrals. The relevant infinite-dimensional variant of Cartan’s moving frame method expressed in quite elementary terms proves to be surprisingly efficient in solution of particular equivalence problems, however, most of the principal questions of the general theory remains unanswered. New concepts of Poincaré-Cartan form and Euler-Lagrange system without Lagrange multiplies appearing as a mere by-product seem to be of independent interest in connection with the 23rd Hilbert problem.
Elements of general theory of infinitely prolonged underdetermined systems of ordinary differential equations are outlined and applied to the equivalence of one-dimensional constrained variational integrals. The relevant infinite-dimensional variant of Cartan’s moving frame method expressed in quite elementary terms proves to be surprisingly efficient in solution of particular equivalence problems, however, most of the principal questions of the general theory remains unanswered. New concepts of Poincaré-Cartan form and Euler-Lagrange system without Lagrange multiplies appearing as a mere by-product seem to be of independent interest in connection with the 23rd Hilbert problem.
Classification : 49J40, 49L99, 58A17, 58E30, 58H05, 70H35
Keywords: constrained variational integral; equivalence problem; diffiety; Poincaré-Cartan form; Frenet coframe 
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Chrastina, Jan. On the equivalence of variational problems. II. Archivum mathematicum, Tome 29 (1993) no. 3-4, pp. 197-220. http://geodesic.mathdoc.fr/item/ARM_1993_29_3-4_a9/

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