  Modern geometric approaches to analytical mechanics rest on a bundle
structure of the configuration space. The connection on this bundle allows for
an intrinsic splitting of the reduced Euler-Lagrange equations. Hamel's
equations, on the other hand, provide a universal approach to non-holonomic
mechanics in local coordinates. The link between Hamel's formulation and
geometric approaches in local coordinates has not been discussed sufficiently.
The reduced Euler-Lagrange equations as well as the curvature of the
connection, are derived with Hamel's original formalism. Intrinsic splitting
into Euler-Lagrange and Euler-Poincare equations, and inertial decoupling is
achieved by means of the locked velocity. Various aspects of this method are
discussed.
