High-order geometric methods for nonholonomic mechanical systems
For researchers in geometric mechanics and robotics, this provides high-order structure-preserving integrators for nonholonomic systems, which are important for simulating vehicles with rolling or sliding contact.
This paper develops high-order geometric integrators for nonholonomic mechanical systems, preserving geometric structures like constraints and energy behavior. The methods are designed for systems with velocity constraints not derivable from position constraints, such as rolling or sliding contact.
In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry associated to the original system as much as possible, such as the structure of the configuration space, the energy behaviour, preservation of constants of the motion and of constraints or other structures associated to the continuous system (symplecticity, Poisson structure...). In this article, we develop high-order geometric (or pseudo-variational) integrators for nonholonomic systems, i.e., mechanical systems subjected to constraint functions which are, roughly speaking, functions on velocities that are not derivable from position constraints. These systems realize rolling or certain kinds of sliding contact and are important for describing different classes of vehicles.