{"id":1124,"date":"2020-11-09T16:05:53","date_gmt":"2020-11-09T19:05:53","guid":{"rendered":"https:\/\/www.ufrgs.br\/ppgmat\/?p=1124"},"modified":"2022-05-24T14:07:11","modified_gmt":"2022-05-24T17:07:11","slug":"webinarios-de-matematica-do-ppgmat-apresenta-a-palestra-first-integrals-and-hamiltonization-of-nonholonomic-systems-the-example-of-a-homogeneous-ball-on-a-convex-surface-of-revolution","status":"publish","type":"post","link":"https:\/\/www.ufrgs.br\/ppgmat\/en\/webinarios-de-matematica-do-ppgmat-apresenta-a-palestra-first-integrals-and-hamiltonization-of-nonholonomic-systems-the-example-of-a-homogeneous-ball-on-a-convex-surface-of-revolution\/","title":{"rendered":"Webin\u00e1rios de Matem\u00e1tica do PPGMat apresenta a palestra &#8220;First integrals and hamiltonization of nonholonomic systems: the example of a homogeneous ball on a convex surface of revolution&#8221;"},"content":{"rendered":"\n<p>Nesta quarta-feira, dia&nbsp;<strong>11\/11\/2020 \u00e0s 14:00<\/strong>, teremos a 12\u00aa edi\u00e7\u00e3o&nbsp;dos&nbsp;Webin\u00e1rios de Matem\u00e1tica do PPGMat &#8211; UFRGS. \u00c9 com prazer que convidamos a todos. Sintam-se \u00e0 vontade para compartilhar esta mensagem.<br>Nossos primeiros webin\u00e1rios j\u00e1 se encontram no YouTube, no&nbsp;<a href=\"https:\/\/www.youtube.com\/channel\/UC7hU77kWUskQWAHK1MwlcGg\" target=\"_blank\" rel=\"noreferrer noopener\">canal do PPGMat<\/a>. Confiram l\u00e1! \ud83d\ude42<br>Informa\u00e7\u00f5es do webin\u00e1rio desta semana:<\/p>\n\n\n\n<p><strong>First integrals and hamiltonization of nonholonomic systems: the example of a homogeneous ball on a convex surface of revolution<\/strong><\/p>\n\n\n\n<p>por&nbsp;<strong>Luis Yapu (IMPA)<\/strong><\/p>\n\n\n\n<p><strong>Data e hora:&nbsp;<\/strong>Quarta-feira, 11 de Novembro de 2020 \u00e0s 14:00<\/p>\n\n\n\n<p><strong>Acesso:&nbsp;<\/strong>Plataforma Google Meet em&nbsp;<a href=\"http:\/\/meet.google.com\/ywh-ybta-fmf\" target=\"_blank\" rel=\"noreferrer noopener\">meet.google.com\/ywh-ybta-fmf<\/a><\/p>\n\n\n\n<p><strong>Resumo:<\/strong>&nbsp;Using the geometric approach to nonholonomic mechanical systems, we will explain the utility of having special first integrals coming from symmetries &nbsp;(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.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nesta quarta-feira, dia&nbsp;11\/11\/2020 \u00e0s 14:00, teremos a 12\u00aa edi\u00e7\u00e3o&nbsp;dos&nbsp;Webin\u00e1rios de Matem\u00e1tica do PPGMat &#8211; UFRGS. \u00c9 com prazer que convidamos a todos. Sintam-se \u00e0 vontade para compartilhar esta mensagem.Nossos primeiros webin\u00e1rios j\u00e1 se encontram no YouTube, no&nbsp;canal do PPGMat. Confiram l\u00e1! \ud83d\ude42Informa\u00e7\u00f5es do webin\u00e1rio desta semana: First integrals and hamiltonization of nonholonomic systems: the example <a href=\"https:\/\/www.ufrgs.br\/ppgmat\/en\/webinarios-de-matematica-do-ppgmat-apresenta-a-palestra-first-integrals-and-hamiltonization-of-nonholonomic-systems-the-example-of-a-homogeneous-ball-on-a-convex-surface-of-revolution\/\" rel=\"nofollow\"><span class=\"sr-only\">Read more about Webin\u00e1rios de Matem\u00e1tica do PPGMat apresenta a palestra &#8220;First integrals and hamiltonization of nonholonomic systems: the example of a homogeneous ball on a convex surface of revolution&#8221;<\/span>[&hellip;]<\/a><\/p>\n","protected":false},"author":1,"featured_media":1072,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/posts\/1124"}],"collection":[{"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/comments?post=1124"}],"version-history":[{"count":1,"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/posts\/1124\/revisions"}],"predecessor-version":[{"id":1125,"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/posts\/1124\/revisions\/1125"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/media\/1072"}],"wp:attachment":[{"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/media?parent=1124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/categories?post=1124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ufrgs.br\/ppgmat\/en\/wp-json\/wp\/v2\/tags?post=1124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}