Lagrangian submanifolds and the Hamilton-Jacobi equation
type: Item
instance of: scholarly article
title: Lagrangian submanifolds and the Hamilton-Jacobi equation
zbMATH Open document ID: 1312.70013
author: M. Barbero-Liñán
author: Manuel de León
author: David Martín de Diego
published in: Monatshefte für Mathematik
publication date: 2013-09-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1209.0807
review text: The authors present a generalized version of the geometric Hamilton-Jacobi theory in terms of certain Lagrangian submanifolds of a symplectic manifold. This allows them to give a unified presentation of Hamilton-Jacobi equations for systems with both holonomic and linear nonholonomic constraints. The formulation treats both the time-independent and the time-dependent case, where the authors need to use a time-dependent family of Lagrangian submanifolds. The application to the linear nonholonomic case gives more general results than those known in the literature. The most interesting feature of the approach in terms of Lagrangian submanifolds is that it gives a unified framework that also allows to deal with singular Lagrangian systems, as shown by \textit{W. M. Tulczyjew} (see, e.g. [C. R. Acad. Sci., Paris, Sér. A 283, 15--18 (1976; Zbl 0327.58007); ibid. A 283, 675--678 (1976; Zbl 0334.58008)]), and can be adapted to even more general settings.
reviewed by: Antonio De Nicola
Mathematics Subject Classification ID: 70H20
Mathematics Subject Classification ID: 70G45
Mathematics Subject Classification ID: 70F20
Mathematics Subject Classification ID: 70F25
zbMATH DE Number: 6210441
zbMATH Keywords: holonomic system
zbMATH Keywords: nonholonomic system
zbMATH Keywords: symplectic manifold
zbMATH Keywords: singular Lagrangian
MaRDI profile type: Publication
OpenAlex ID: W2090816497
arXiv ID: 1209.0807
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DOI: 10.1007/S00605-013-0522-1
description: scientific article; zbMATH DE number 6210441