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dc.contributor.advisorCelledoni, Elenanb_NO
dc.contributor.authorHilden, Sindre Kristensennb_NO
dc.date.accessioned2014-12-19T13:58:08Z
dc.date.available2014-12-19T13:58:08Z
dc.date.created2010-09-04nb_NO
dc.date.issued2009nb_NO
dc.identifier348822nb_NO
dc.identifierntnudaim:4739nb_NO
dc.identifier.urihttp://hdl.handle.net/11250/258511
dc.description.abstractWe discuss nonholonomic systems in general and numerical methods for solving them. Two different approaches for obtaining numerical methods are considered; discretization of the Lagrange-d'Alembert equations on the one hand, and using the discrete Lagrange-d'Alembert principle to obtain nonholonomic integrators on the other. Among methods using the first approach, we focus on the super partitioned additive Runge-Kutta (SPARK) methods. Among nonholonomic integrators, we focus on a reversible second order method by McLachlan and Perlmutter. Through several numerical experiments the methods we present are compared by considering error-growth, conservation of energy, geometric properties of the solution and how well the constraints are satisfied. Of special interest is the comparison of the 2-stage SPARK Lobatto IIIA-B method and the nonholonomic integrator by McLachlan and Perlmutter, which both are reversible and of second order. We observe a clear connection between energy-conservation and the geometric properties of the numerical solution. To preserve energy in long-time integrations is seen to be important in order to get solutions with the correct qualitative properties. Our results indicate that the nonholonomic integrator by McLachlan and Perlmutter sometimes conserves energy better than the 2-stage SPARK Lobatto IIIA-B method. In a recent work by Jay, however, the same two methods are compared and are found to conserve energy equally well in long-time integrations.nb_NO
dc.languageengnb_NO
dc.publisherInstitutt for matematiske fagnb_NO
dc.subjectntnudaimno_NO
dc.subjectSIF3 fysikk og matematikkno_NO
dc.subjectIndustriell matematikkno_NO
dc.titleNumerical Methods for Nonholonomic Mechanicsnb_NO
dc.typeMaster thesisnb_NO
dc.source.pagenumber76nb_NO
dc.contributor.departmentNorges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fagnb_NO


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