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Mathematics 2018, 6(9), 163; https://doi.org/10.3390/math6090163

Higher Order Hamiltonian Systems with Generalized Legendre Transformation

Department of Informatics and Natural Sciences, Institute of Technology and Business, Okružní 517/10, 370 01 České Budějovice, Czech Republic
Received: 9 August 2018 / Revised: 27 August 2018 / Accepted: 4 September 2018 / Published: 10 September 2018
(This article belongs to the Special Issue Differential Geometry of Special Mappings)
Full-Text   |   PDF [247 KB, uploaded 10 September 2018]

Abstract

The aim of this paper is to report some recent results regarding second order Lagrangians corresponding to 2nd and 3rd order Euler–Lagrange forms. The associated 3rd order Hamiltonian systems are found. The generalized Legendre transformation and geometrical correspondence between solutions of the Hamilton equations and the Euler–Lagrange equations are studied. The theory is illustrated on examples of Hamiltonian systems satisfying the following conditions: (a) the Hamiltonian system is strongly regular and the Legendre transformation exists; (b) the Hamiltonian system is strongly regular and the Legendre transformation does not exist; (c) the Legendre transformation exists and the Hamiltonian system is not regular but satisfies a weaker condition. View Full-Text
Keywords: Hamilton equations; Lagrangian; regular and strongly regular systems Hamilton equations; Lagrangian; regular and strongly regular systems
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Smetanová, D. Higher Order Hamiltonian Systems with Generalized Legendre Transformation. Mathematics 2018, 6, 163.

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