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

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a
stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to …

The optimal control of a mechanical system is of crucial importance in many application
areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a …

The equations of motion of a controlled mechanical system subject to holonomic constraints
may be formulated in terms of the states and controls by applying a constrained version of …

This paper presents a Lie–Trotter splitting for inertial Langevin equations (geometric
Langevin algorithm) and analyzes its long-time statistical properties. The splitting is defined …

Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models,
we present a general framework for introducing stochasticity into variational principles …

We introduce a new class of integrators for stiff ODEs as well as SDEs. Examples of
subclasses of systems that we treat are ODEs and SDEs that are sums of two terms, one of …

In this paper, we describe and exploit a geometric framework for Gibbs probability densities
and the associated concepts in statistical mechanics, which unifies several earlier works on …

We use the global stochastic analysis tools introduced by PA Meyer and L. Schwartz to write
down a stochastic generalization of the Hamilton equations on a Poisson manifold that, for …

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 …