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Dalla Via, Marco (2017) Geometric and dynamic phase-space structure of a class of nonholonomic integrable systems with symmetries. [Magistrali biennali]

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Abstract

This work studies a certain class of nonholonomic mechanical systems: a sphere which rolls without sliding inside a rotating convex surface. We study the dynamics of the system, performing some reductions by symmetry, and we consider the reduced system which has 3 first integrals. We prove that these 3 first integrals are functionally independent and we use them to show that, for a certain choice of the surface profile, the reduced dynamics is periodic and the ureduced dynamics is quasi-periodic. Next we consider the case in which the surface is a known profile, a paraboloid of revolution, and we explicitly build the 3 first integrals in order to use them to have a better understanding of the reduced dynamics. We restrict the reduced dynamics to the common level sets of 2 of the first integrals: we show that the restricted systems are 2-parameters Lagrangian systems with 1 degree of freedom. Next we realize a numerical analysis to study the equilibria of this family of Lagrangian systems and we show the appearance of stable and unstable equilbria with a bifurcation mechanism, as we change the values of the parameters.

Item Type:Magistrali biennali
Corsi di Diploma di Laurea:Scuola di Scienze > Fisica
Uncontrolled Keywords:Nonholonomic mechanics, symmetries, first integrals, integrability
Subjects:Area 02 - Scienze fisiche > FIS/02 Fisica teorica, modelli e metodi matematici
Codice ID:56985
Relatore:Fassò, Francesco
Correlatore:Sansonetto, Nicola
Data della tesi:September 2017
Biblioteca:Polo di Scienze > Dip. Fisica e Astronomia "Galileo Galilei" - Biblioteca
Tipo di fruizione per il documento:on-line per i full-text
Tesi sperimentale (Si) o compilativa (No)?:Yes

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