Optimal control theory and Newton–Euler formalism for Cosserat beam theory

Georges Le Vey

doi:10.1016/j.crme.2006.01.006

Optimal control theory and Newton–Euler formalism for Cosserat beam theory
[Commande optimale et formalisme de Newton–Euler pour les poutres de Cosserat]

Présenté par : Charles-Michel Marle

Georges Le Vey ¹

¹ IRCCyN-UMR CNRS 6597, École des mines de Nantes, 4, rue A. Kastler, 44307 Nantes cedex 1, France

Comptes Rendus. Mécanique, Volume 334 (2006) no. 3, pp. 170-175.

Résumé
Abstract

Un formalisme de Newton–Euler pour les théories de poutres de Cosserat est obtenu de manière purement déductive, grâce à une analogie avec la théorie de la commande optimale. La méthode repose sur l'utilisation conjointe du principe de la moindre contrainte de Gauss, des équations d'Appell et de la théorie de la commande optimale, de façon analogue à un travail précédent sur le formalisme de Newton–Euler bien connu pour les systèmes multicorps.

A Newton–Euler formalism is derived for Cosserat beam theory in a purely deductive manner, thanks to an analogy with optimal control theory. The method relies upon joint use of Gauss least constraint principle, Appell's equations and optimal control theory, that was used successfully in a previous work for the classical case of discrete Newton–Euler backward and forward recursions of multibody systems.

Reçu le : 2005-07-07
Accepté le : 2006-01-19
Publié le : 2006-02-24

DOI : 10.1016/j.crme.2006.01.006

Keywords: Dynamics of rigid or flexible systems, Newton–Euler, Gauss principle, Appell's equations, Optimal control
Mots-clés : Dynamique des systèmes rigides ou flexibles, Newton–Euler, principe de Gauss, équations d'Appell, Commande optimale

Affiliations des auteurs :

Georges Le Vey ¹

¹ IRCCyN-UMR CNRS 6597, École des mines de Nantes, 4, rue A. Kastler, 44307 Nantes cedex 1, France

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Georges Le Vey. Optimal control theory and Newton–Euler formalism for Cosserat beam theory. Comptes Rendus. Mécanique, Volume 334 (2006) no. 3, pp. 170-175. doi : 10.1016/j.crme.2006.01.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.01.006/

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Cité par 7 documents. Sources : Crossref

^⁎ This work was supported by the French CNRS ROBEA program.

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