Kinematic reduction and the Hamilton-Jacobi equation
  A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces. 
Mar\'ia Barbero-Li\~n\'an and Manuel de Le\'on and Juan Carlos Marrero   and David Mart\'in de Diego and Miguel C. Mu\~noz-L...
math-ph math.DG math.MP math.OC