A hierarchy of non-holonomic constraints and step-2 nilpotent lie algebras

We consider a hierarchy of non-holonomic con- straints defined by means of Pfaffian systems of differential 1-forms, that yield driftless control systems affine in the con- trols. The first level of the hierarchy produces driftless control systems defined by distributions of vectors fields determining step-2 nilpotent Lie algebras that can be studied by standard geometric control theory methods. We present the case of the six dimensional Lie algebra that models a classical particle in a three-dimensional space in a homogeneous magnetic field with arbitrary direction.