Accurate numerical simulation of dynamical systems is essential in applications ranging
from particle physics to geophysical fluid flow to space hazard analysis. However, most …

The Collaborative Research Centre 614" Self-Optimizing Concepts and Structures in
Mechanical Engineering", funded from 2002 to 2013 by the German Research Foundation …

We propose a new framework of Hessian-free force-gradient integrators that do not require
the analytical expression of the force-gradient term based on the Hessian of the potential …

In this work we derive and analyze variational integrators of higher order for the structure-
preserving simulation of mechanical systems. The construction is based on a space of …

The goal of this paper is to derive a structure preserving integrator for geometrically exact
beam dynamics, by using a Lie group variational integrator. Both spatial and temporal …

In this work, the equivalence of Galerkin variational integrators and Runge–Kutta methods is
studied. The construction of Galerkin variational integrators relies on the approximation of …

In this work, variational integrators of higher order for dynamical systems with holonomic
constraints are constructed and analyzed. The construction is based on approximating the …

In recent years, much effort in designing numerical methods for the simulation and
optimization of mechanical systems has been put into schemes which are structure …

This article uses physical arguments to derive variational integration schemes for dissipative
mechanical systems. These integration algorithms find utility in the solution of the equations …

In recent years that has been a worldwide increase in the utilisation of Autonomous
Underwater Vehicles (AUVs) for many diverse subsea applications. This has given rise to an …