Nesta quarta-feira, dia 11/11/2020 às 14:00, teremos a 12ª edição dos Webinários de Matemática do PPGMat – UFRGS. É com prazer que convidamos a todos. Sintam-se à vontade para compartilhar esta mensagem.
Nossos primeiros webinários já se encontram no YouTube, no canal do PPGMat. Confiram lá! 🙂
Informações do webinário desta semana:
First integrals and hamiltonization of nonholonomic systems: the example of a homogeneous ball on a convex surface of revolution
por Luis Yapu (IMPA)
Data e hora: Quarta-feira, 11 de Novembro de 2020 às 14:00
Acesso: Plataforma Google Meet em meet.google.com/ywh-ybta-fmf
Resumo: Using the geometric approach to nonholonomic mechanical systems, we will explain the utility of having special first integrals coming from symmetries (or horizontal gauge momenta) in order to obtain a hamiltonian formulation of the reduced dynamics (hamiltonization). The main result gives sufficient conditions on the horizontal gauge momenta in order to obtain a twisted-Poisson (or sometimes Poisson) structure in the reduced space using the method of gauge transformations by a 2-form, which has explicit expressions. The leaves of the reduced (twisted-)Poisson structure are given by the joint level sets of casimirs coming from the first integrals. We will focus on the example of a homogenous ball rolling on a convex surface of revolution to illustrate the theory. This is a joint work with Paula Balseiro.