On the geometry of the Schmidt-Legendre transformation

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doi:10.3934/jgm.2018010

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2018, Volume 10, Issue 3: 251-291. Doi: 10.3934/jgm.2018010

This issue Previous Article Next Article The Euler-Poisson equations: An elementary approach to integrability conditions

On the geometry of the Schmidt-Legendre transformation

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1.
Department of Mathematics, Gebze Technical University, 41400 Çayırova, Gebze, Kocaeli, Turkey
2.
S.N. Bose National Centre for Basic Sciences, JD Block, Sector Ⅲ, Salt Lake, Kolkata - 700098, India

* Corresponding author
* Corresponding author

Received: January 31, 2017

Revised: July 31, 2018

Published: August 2018

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Abstract

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.

Keywords:

Ostrogradsky-Legendre transformation,
Schmidt-Legendre transformation,
second order degenerate Lagrangian systems,
Tulczyjew's triple.

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

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References

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