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We present an application of a recently introduced variant of orbit spacereduction for symmetric dynamical systems. This variant works with suitablelocalizations of the algebra of polynomial invariants of the group actions, andprovides reduction to a variety that is embedded in a low-dimensional affinespace, which makes efficient computations possible. As an example, we discussthe mechanical system of a "barbell" in a central force field.

A "barbell" in a central force field: A case study in symmetry reduction