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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.1994.tde-20210729-005440
Document
Author
Full name
Mario Tirone
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1994
Supervisor
Title in Portuguese
Mecânica vakonomica-um novo modelo para a mecânica analítica
Keywords in Portuguese
Mecânica Clássica
Abstract in Portuguese
não disponível
Title in English
not available
Abstract in English
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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Publishing Date
2021-07-29
 
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