This paper gives a review of integration algorithms for finite dimensional mechanical
systems that are based on discrete variational principles. The variational technique gives a …

The purpose of this paper is to survey some recent advances in variational integrators for
both finite dimensional mechanical systems as well as continuum mechanics. These …

The use of the symmetries of a physical system in the study of its dynamics has a long
history that goes back to the founders of c1assical mechanics. Symmetry-based tech niques …

In this volume readers will find for the first time a detailed account of the theory of symplectic
reduction by stages, along with numerous illustrations of the theory. Special emphasis is …

This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a
way that allows the reduction process to be repeated; that is, it develops a context for …

We develop the equations of motion for full body models that describe the dynamics of rigid
bodies, acting under their mutual gravity. The equations are derived using a variational …

This paper outlines some features of general reduction theory as well as the geometry of
nonholonomic mechanical systems. In addition to this survey nature, there are some new …

Equations of motion, referred to as full body models, are developed to describe the
dynamics of rigid bodies acting under their mutual gravitational potential. Continuous …

This dissertation studies the dynamics and optimal control of rigid bodies from two
complementary perspectives, by providing theoretical analyses that respect the fundamental …

Variational integrators are a class of discretizations for mechanical systems which are
derived by discretizing Hamilton's principle of stationary action. They are applicable to both …