  In optimal control problems, there exist different kinds of extremals, that
is, curves candidates to be solution: abnormal, normal and strictly abnormal.
The key point for this classification is how those extremals depend on the cost
function. We focus on control systems such as nonholonomic control mechanical
systems and the associated kinematic systems as long as they are equivalent.
  With all this in mind, first we study conditions to relate an optimal control
problem for the mechanical system with another one for the associated kinematic
system. Then, Pontryagin's Maximum Principle will be used to connect the
abnormal extremals of both optimal control problems.
  An example is given to glimpse what the abnormal solutions for kinematic
systems become when they are considered as extremals to the optimal control
problem for the corresponding nonholonomic mechanical systems.
