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On the geometry of the Schmidt-Legendre transformation

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  • Tulczyjew's triples are constructed for the Schmidt-Legendre transformations of both second and third-order Lagrangians. Symplectic diffeomorphisms relating the Ostrogradsky-Legendre and the Schmidt-Legendre transformations are derived. Several examples are presented.

    Mathematics Subject Classification: Primary: 70H50; Secondary: 70H45.

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