  We provide a new and simple system of equations for the normal sub-Riemannian
geodesics. These use a partial connection that we show is canonically
available, given a choice of complement to the distribution. We also describe
conditions which, if satisfied, mean that even this choice of complement is
determined canonically, and that this determines a distinguished connection on
the tangent bundle.
  Our approach applies to sub-Riemannian geometry the point of view of
non-holonomic mechanics. The geodesic equations obtained split into mutually
driving horizontal and complementary parts, and the method allows for
particular choices of nice coframes. We illustrate this feature on examples of
contact models with non-constant symbols.
