  Hybrid systems are dynamical systems with continuous-time and discrete-time
components in their dynamics. When hybrid systems are defined on a principal
bundle we are able to define two classes of impacts for the discrete-time
transition of the dynamics: interior impacts and exterior impacts. In this
paper we define hybrid systems on principal bundles, study the underlying
geometry on the switching surface where impacts occur and we find conditions
for which both exterior and interior impacts are preserved by the mechanical
connection induced in the principal bundle.
