41 citations · 155 across the 18 of their papers we have counts for
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Superconvergence of Galerkin variational integrators
Sina Ober-Blöbaum, Mats Vermeeren
We study the order of convergence of Galerkin variational integrators for ordinary differential equations. Galerkin variational integrators approximate a variational (Lagrangian) p…
Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics
Luis C. García-Naranjo, Mats Vermeeren
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…
Numerical integration in celestial mechanics: a case for contact geometry
Alessandro Bravetti, Marcello Seri, Mats Vermeeren +1
Several dynamical systems of interest in celestial mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, th…
Contact variational integrators
Mats Vermeeren, Alessandro Bravetti, Marcello Seri
We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a…
Modified equations for variational integrators applied to Lagrangians linear in velocities
Mats Vermeeren
Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of…
Numerical precession in variational discretizations of the Kepler problem
Mats Vermeeren
Kepler's first law states that the orbit of a point mass with negative energy in a classical gravitational potential is an ellipse with one of its foci at the gravitational center.…
Modified Equations for Variational Integrators
Mats Vermeeren
It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamil…