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The contact transformation groups of the Extended Hamiltonian System

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Abstract

The 1-parameter transformation groups (otherwise known as infinitesimal transformations) admitted by a system of differential equations are fundamental to the study of its properties. In this paper we first of all consider 1-parameter groups of contact transformations. Then, by generalizing Noether's theorem, we show how they are fundamental to what I call the Extended Hamiltonian System. Finally, this is illustrated by the extendedN-Body problem.

Resume

Les groupes de transformations à 1 paramètre (appelés aussi transformations infinitésimales) admis par un systeme d'équations différentielles sont fondamentaux dans l'étude de ses propriétés. Dans cet article, nous considérons d'abord les groupes à 1 paramètre de transformations de contact. Ensuite, par la généralisation du théorème de Noether, nous montrons qu'ils sont fondamentaux dans l'étude de ce que j'appelle le Système Hamiltonien Etendu. Enfin ceci est illustré par le problème étendu desN-Corps.

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  1. Laboratoire de Mécanique Théorique, Faculté des Sciences et des Techniques, 25030, Besançon Cédex, France

    J. Bryant

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  1. J. Bryant
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Bryant, J. The contact transformation groups of the Extended Hamiltonian System. Celestial Mechanics 25, 41–49 (1981). https://doi.org/10.1007/BF01301805

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  • DOI: https://doi.org/10.1007/BF01301805

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