  Euler-Lagrange equations and variational integrators are developed for
Lagrangian mechanical systems evolving on a product of two-spheres. The
geometric structure of a product of two-spheres is carefully considered in
order to obtain global equations of motion. Both continuous equations of motion
and variational integrators completely avoid the singularities and complexities
introduced by local parameterizations or explicit constraints. We derive global
expressions for the Euler-Lagrange equations on two-spheres which are more
compact than existing equations written in terms of angles. Since the
variational integrators are derived from Hamilton's principle, they preserve
the geometric features of the dynamics such as symplecticity, momentum maps, or
total energy, as well as the structure of the configuration manifold.
Computational properties of the variational integrators are illustrated for
several mechanical systems.
