Reduction by Stages via Symplectic Distributions

In the remaining two chapters of this part we are going to take a different technical approach to the reduction by stages problem. It will be mainly based on thinking of the (connected components of the) level sets of the various momentum maps in the setup as the accessible sets of a distribution that we will introduce in the following paragraphs. This point of view has been exploited in Ortega [2002] and Ortega and Ratiu [2002, 2004a] in the context of the so-called optimal momentum map.