A geometrization and generalization of the Routh procedure of Lagrangian reduction is presented. This is done by including conservative gyroscopic forces into the variational principle. A Dirac constraint type of construction occurs useful as one of the aids for the nonabelian case. The rigid body as a simple nonabelian example is discussed. The general techniques of geometric mechanics is applied to the double spherical pendulum, that is a mechanical system with an abelian symmetry group. Lagrangian reduction methods are used in this case to get the linearized equations that enable one to detect bifurcations (such as the Hamilton- Hopf bifurcation). The authors expect that the methods of this paper can be applied to a number of other situations as well, such as pseudo-rigid bodies, etc.