Abstract
In this paper we consider the controllability problem for systems defined on principal fibre bundles, in which the set of associated vector fields is invariant under the action of the structure group, and projects down on to a set of vector fields on the base space. It is shown that if the system is accessible, and the structure group is compact, then the system is controllable if and only if the system is controllable when projected onto the base space. The connection between these systems and systems admitting symmetries generated by free and proper group actions is described, and various examples are given relating to systems on homogeneous spaces.
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