Regularity of generating families of functions

Włodzimierz M. Tulczyjew; Paweł Urbański

doi:10.3934/jgm.2010.2.199

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2010, Volume 2, Issue 2: 199-221. Doi: 10.3934/jgm.2010.2.199

This issue Previous Article Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics Next Article

Regularity of generating families of functions

Włodzimierz M. Tulczyjew^1, and
Paweł Urbański^2,

1.
Valle San Benedetto, 2, 62030 Monte Cavallo
2.
Division of Mathematical Methods in Physics, University of Warsaw, Hoża 74, 00-682 Warszawa

Received: January 31, 2010

Revised: May 31, 2010

Published: May 2010

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Abstract

We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be generated by a family of functions. We discuss conditions, under which a family of functions generates an immersed Lagrangian submanifold. These conditions are given in terms of the Hessian of the family.

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Mathematics Subject Classification: Primary: 53D12, 70G75; Secondary: 70H99, 49S05.

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