  Hybrid (and impact) systems are dynamical systems experiencing both
continuous and discrete transitions. In this work, we derive necessary and
sufficient conditions for when a given differential form is invariant, with
special attention paid to the case of the existence of invariant volumes.
Particular attention is given to impact systems where the continuous dynamics
are Lagrangian and subject to nonholonomic constraints. Additionally, we
demonstrate that the existence of a smooth invariant volume severely inhibits
Zeno behavior.
