Hamel's Formalism and Variational Integrators on a Sphere
  This paper discusses Hamel's formalism and its applications to structure-preserving integration of mechanical systems. It utilizes redundant coordinates in order to eliminate multiple charts on the configuration space as well as nonphysical artificial singularities induced by local coordinates, while keeping the minimal possible degree of redundancy and avoiding integration of differential-algebraic equations. 
Dmitry V. Zenkov, Melvin Leok, Anthony M. Bloch
math.NA