Mechanical Systems: Symmetry and Reduction

Marsden, J. E. and T. S. Ratiu

Encyclopedia of Complexity and Systems Science, 6, (2009), 5482-5510

Abstract:

Reduction theory is concerned with mechanical systems with symmetries. It constructs a lower dimensional reduced space in which associated conservation laws are taken out and symmetries are “factored out” and studies the relation between the dynamics of the given system with the dynamics on the reduced space. This subject is important in many areas, such as stability of relative equilibria, geometric phases and integrable systems.