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An expression of classical dynamics

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An expression of classical dynamics ANNALES DE L’I. H. P., SECTION C J.-J. MOREAU An expression of classical dynamics Annales de l’I. H. P., section C, tome S6 (1989), p. 1-48. <> © Gauthier-Villars, 1989, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section C » (, implique l’accord avec les condi- tions générales d’utilisation ( Toute uti- lisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit conte- nir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques AN EXPRESSION OF CLASSICAL DYNAMICS J.-J. MOREAU Laboratoire de Mécanique Générale des Milieux Continus, Unité associée au C.N.R.S.1214, Université des Sciences et Techniques du Languedoc, Montpellier, France. b s tr a t , The proposed formulation extends the Euler variable approach, classical in Continuum Mechanics, up to make it val id for such singular systems as, for instance, a single mass-point. The key concept is the kinetic tensor measure of the investigated material, relative to some wi~dow~ in time-space. This 1s f irst developed In the framework of GaH lean time-space. I n that case, the fundamental 1 equation involves the four- -dimensional vector distribution divergence of the kinetic tensor measure. It is shown, in particular, how the Initial conditions of an evolution problem or th~ confinement of the investigated system by a given boundary, possibly with shocks, may be described through adequate terms in the fundamental equation, In order to develop similar procedures in the R i eman- nian manifold setting of Analytical Dynamics, one introduces the diffe- rential operator equilibrium, acting on the doubly contravariant symmetric tensor measures of the manifold. This operato

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