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Canonical and Anti-Canonical Transformations Preserving Convexity of Potentials

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2011
auteur(s) Vallee Claude; Hjiaj Mohammed; Fortuné Danielle; De Saxce Géry
journal (abréviation) Journal of Elasticity (J Elasticity)
volume (numéro) 103 (2)
  
pages 247 – 267
résumé The aim of the paper is to characterize transformations that preserve the potential structure of a relationship between dual variables. The first step consists in deriving a geometric definition of the condition for the existence of a potential. Having at hand this formulation, it becomes clear that the canonical similitudes represents the class of transformations that preserves the potential form of a relationship. Next, we derive the conditions under which canonical similitudes preserve the convexity of the potential or change it into concavity. This new class of transformations can be viewed as a generalization of the Legendre-Fenchel transformation. These concepts are applied to the Hooke constitutive relationship.
mots clés Elastic potential; Symplectic geometry; Canonical and symplectic transformations; Convexity
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