A new variational integrator is proposed to solve constrained mechanical systems. The main
distinguishing feature of the present integrator comes from the distinct discretization of …

Variational integration approaches are favorable for long-time simulations, due to their
remarkable symplectic and momentum conservation properties, as well as the nearly energy …

Contact Hamiltonian systems are a generalization of the Hamiltonian systems of classical
mechanics. The action is added as an extra variable in phase space, and symplectic …

In previous work a variational integration scheme for mechanical systems containing linear
dissipation was developed (Limebeer et al., 2020). The key idea is to use a transmission line …

arXiv:2103.14418v2 [math.DG] 12 Jul 2021 Page 1 arXiv:2103.14418v2 [math.DG] 12 Jul 2021
LOCAL CONVEXITY FOR SECOND ORDER DIFFERENTIAL EQUATIONS ON A LIE ALGEBROID …

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 …

Based on the Lagrange–d'Alembert principle and a modified Lagrange–d'Alembert
principle, two kinds of symmetric algorithms with arbitrary high order are proposed for non …

We propose a discretization of vector fields that are Hamiltonian up to multiplication by a
positive function on the phase space that may be interpreted as a time reparametrization …

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 …