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Mémoire de Maîtrise
DOI
https://doi.org/10.11606/D.45.1994.tde-20210729-005440
Document
Auteur
Nom complet
Mario Tirone
Adresse Mail
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Paulo, 1994
Directeur
Titre en portugais
Mecânica vakonomica-um novo modelo para a mecânica analítica
Mots-clés en portugais
Mecânica Clássica
Resumé en portugais
não disponível
Titre en anglais
not available
Resumé en anglais
We will study a new model to describe motions of material points when they are exposed to external forces and constraints, specially non-integrable ones. This model, called vakonomic mechanics, is based on the hamilton principle (principle of least action) with a new set of variations of a curve considered. It was introduced by v.V. Kozlov and v.I. Arnold and when there are only integrable constraints it is reduced to the known model. We show in chapter 1 a short, but wide, review of the classical lagrangian mechanics, based on the d'alembert-lagrange principle. In chapter 2. We introduce the vakonomic mechanics, and show an exemple comparing its result with the lagrangian mechanics one. It has also some new facts that were not known up to now, specially related to the lost of principle of determinacy. In this chapter we also include a proof of a fundamental theoremin vakonomic mechanics. On the last chapter, we caracterize the existence of equilibrium points in this new model, when the forces envolved have a potential function. We also study their liapunov stability in some cases
 
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TironeMario.pdf (6.31 Mbytes)
Date de Publication
2021-07-29
 
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