A nonholonomic Newmark method

FERRARO, SEBASTIÁN JOSÉ; ANAHORY SIMOES, ALEXANDRE; MARRERO, JUAN CARLOS; MARTÍN DE DIEGO, DAVID

Neuquén

Congreso; Reunión Anual de la UMA, LXXI Reunión de Comunicaciones Científicas; 2022

UMA

Using the nonholonomic exponential map, we obtain a new version of Newmark-type methods for nonholonomic systems (see also [1] for a different extension). We give numerical examples including a test problem where the structure of reversible integrability responsible for good energy behavior as described in [2] is lost. We observe that the composition of two Newmark methods is able to nevertheless produce good energy behaviour on this test problem.Referencias[1] Laurent O. Jay and Dan Negrut. A second order extension of the generalized-α method for constrained systems in mechanics. In Multibody dynamics, volume 12 of Comput. Methods Appl. Sci., pages 143-158. Springer, Berlin, 2009.[2] K Modin and O. Verdier. What makes nonholonomic integrators work? Numer. Math., 145:405-435, 2020.En conjunto con:Alexandre Anahory Simoes (Instituto de Ciencias Matemáticas, ICMAT c/ Nicolás Cabrera, no 13-15, Campus Cantoblanco, UAM 28049 Madrid, Spain)Juan Carlos Marrero (ULL-CSIC Geometrı́a Diferencial y Mecánica Geométrica, Departamento de Matemáticas, Estadı́stica e IO, Instituto Universitario de Matemáticas y Aplicaciones de la ULL, IMAULL, Tenerife, Canary Islands, Spain)David Martı́n de Diego (Instituto de Ciencias Matemáticas, ICMAT c/ Nicolás Cabrera, no 13-15, Campus Cantoblanco, UAM 28049 Madrid, Spain)