A nonholonomic Newmark method

Abstract

Using the nonholonomic exponential map, we obtain a new version of Newmark-type methods for nonholonomic systems (see also Jay and Negrut(2009) for a different extension). We give numerical examples including a test problem where the structure of reversible integrability responsible for good energy behaviour as described in Modin and Verdier (2020) is lost. We observe that the composition of two Newmark methods is able to produce good energy behaviour on this test problem.