NOTE ON THE THEORY OF EUCLIDEAN ACTION
(1866 - 1931)
Université de Toulouse, www.univ-tlse1.fr
31042 Toulouse, France
French Mathematical Society (1913 – President), http://smf.emath.fr
75231 Paris, France
Represented by a Academician of RANS V.I. Erofeev 10.06.2013
This issue of RENSIT publishes the bibliographic rarity - a big labor of brothers Cosserat "Une note sur la théorie de l'action Euclidienne" – the only one to date the work of these authors, published entirely in 1911 in Russian as an appendix to «Traité de mécanique rationnelle» Paul Emile Appel, in Russian translation - three-volume "Rukovodstvo teoreticheskoy (ratsionalnoy) mekhaniki”, and no longer reprinted. About this Annex, in the Preface to his two-volume Traité P.E. Appel writes: "The main interest of this new volume (the second volume in the French edition - Editor's note) is wonderful "Une note sur la théorie de l'action Euclidienne" ... E. and F. Cosserat. ... The purpose of Note - combine different mechanical theories into one general idea from which they are derived deductively, an idea that could serve as a tool for new discoveries. It is known that in modern mechanics the energy dominates ... and the action. E. and F. Cosserat dedicated their works to concept of action, whose value is derived of the Hamilton and Helmholtz theories; they managed to achieve in these theories of new and important success, extract from them all the most significant and establish a direct definition of the action, the form of which may be transferred in all areas of natural philosophy. …The reader will see, to what of the success they have achieved and how their method led them by the right way to the various problems of statics and dynamics relating to the deformable line, deformable surface, deformable medium, with all by private by cases, that considered in geometry and in mechanics. …I am happy to express here to Messrs. E. and F. Cosserat a my gratitude for their gentilesse publish the your beauteous labor at the end of my Guide Mechanics."
Keywords: action, invariant, group, Euclidean displacements.
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