On Geometry of Schmidt Legendre Transformation
O\u{g}ul Esen, Partha Guha
TL;DR
This paper presents a geometric framework for the Schmidt-Legendre transformation of second order Lagrangians using Tulczyjew's triplet, establishing a symplectic relation with Ostrogradsky-Legendre transformation and illustrating with examples.
Contribution
It introduces a geometric approach to Schmidt-Legendre transformation by constructing a Tulczyjew triplet, linking it to Ostrogradsky-Legendre transformation, and providing concrete examples.
Findings
Established a symplectic relation between transformations.
Developed a geometric framework using Tulczyjew's triplet.
Presented multiple illustrative examples.
Abstract
A geometrization of Schmidt-Legendre transformation of the second order Lagrangians is proposed by building a proper Tulczyjew's triplet. The symplectic relation between Ostrogradsky-Legendre and Schmidt-Legendre transformations is obtained. Several examples are presented.
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