On the geometry of the schmidt-legendre transformation

Oğul Esen; Partha Guha

doi:10.3934/jgm.2018010

On the geometry of the schmidt-legendre transformation

Oğul Esen, Partha Guha

Mathematics

Gebze Technical University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	British English
Pages (from-to)	251-291
Number of pages	41
Journal	Journal of Geometric Mechanics
Volume	10
Issue number	3
DOIs	https://doi.org/10.3934/jgm.2018010
State	Published - Sep 2018

Keywords

Ostrogradsky-Legendre transformation
Schmidt-Legendre transformation
Second order degenerate Lagrangian systems
Tulczyjew's triple

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10.3934/jgm.2018010

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title = "On the geometry of the schmidt-legendre transformation",

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",

author = "Oğul Esen and Partha Guha",

note = "Publisher Copyright: {\textcopyright} American Institute of Mathematical Sciences.",

year = "2018",

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doi = "10.3934/jgm.2018010",

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AU - Esen, Oğul

AU - Guha, Partha

N1 - Publisher Copyright: © American Institute of Mathematical Sciences.

PY - 2018/9

Y1 - 2018/9

N2 - 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.

AB - 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.

KW - Ostrogradsky-Legendre transformation

KW - Schmidt-Legendre transformation

KW - Second order degenerate Lagrangian systems

KW - Tulczyjew's triple

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DO - 10.3934/jgm.2018010

M3 - Article

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SP - 251

EP - 291

JO - Journal of Geometric Mechanics

JF - Journal of Geometric Mechanics

IS - 3

ER -

On the geometry of the schmidt-legendre transformation

Abstract

Keywords

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