See also GEOMETRIC MECHANICS—Part II: Rotating, Translating and Rolling (2nd Edition)
This textbook introduces the tools and language of modern geometric mechanics to …

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 …

We give a short and elementary introduction to Lie group methods. A selection of
applications of Lie group integrators are discussed. Finally, a family of symplectic integrators …

We consider the optimal control of mechanical systems on Lie groups and develop
numerical methods that exploit the structure of the state space and preserve the system …

This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian
systems on manifolds, akin to the Ornstein–Uhlenbeck theory of Brownian motion in a force …

A new variational principle for mechanical systems subject to holonomic constraints is
presented. The newly proposed GGL principle is closely related to the often used Gear …

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 …

This study derives geometric, variational discretization of continuum theories arising in fluid
dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central …

Many nonlinear systems of practical interest evolve on Lie groups or on manifolds acted
upon by Lie groups. Examples range from aircraft and underwater vehicles to quantum …