# Lagrangian Reduction and the Double Spherical Pendulum

**Marsden, J. E., and J. Scheurle
**

Dedicated to Klaus Kirchgässner for his 60th Birthday

*ZAMP* **44**, 17-43.

### Abstract:

This paper studies the stability and bifurcations of the relative equilibria
of the double spherical pendulum, which has the circle as its symmetry group. This example as
well as others with nonabelian symmetry groups, such as the rigid body, illustrate some useful
general theory about Lagrangian reduction. In particular, we establish a
satisfactory global theory of Lagrangian reduction that is consistent with the classical
local Routh theory for systems with an abelian symmetry group.