Geometric mechanics

Geometric mechanics is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid bodies to fluid mechanics to control theory.

Geometric mechanics applies principally to systems for which the configuration space is a Lie group, or a group of diffeomorphisms, or more generally where some aspect of the configuration space has this group structure. For example, the configuration space of a rigid body such as a satellite is the group of Euclidean motions (translations and rotations in space), while the configuration space for a liquid crystal is the group of diffeomorphisms coupled with an internal state (gauge symmetry or order parameter).