Geometric mechanics is a fairly recent field of mathematics lying in the intersection of at least
four different scientific fields: differential geometry, physics, numerical analysis and …

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 …

In this paper, we prove that the trajectories of unreduced $\phi $-simple Chaplygin kinetic
systems are reparametrizations of horizontal geodesics with respect to a modified …

For a Lagrangian system with nonholonomic constraints, we construct extensions of the
equations of motion to sets of second-order ordinary differential equations. In the case of a …

In this paper, we define Jacobi fields for nonholonomic mechanics using a similar
characterization than in Riemannian geometry. We give explicit conditions to find Jacobi …

Using the nonholonomic exponential map, we generalize the well-known family of Newmark
methods for nonholonomic systems. We give numerical examples including a test problem …