Mechanical systems with time-varying topology appear frequently in natural or human-made artificial systems. The nature of topology transitions is a key characteristic in the functioning of such systems. In this paper, we discuss a concept that can offer possibilities to gain insight and analyze topology transitions. This approach relies on the use of impulsive constraints and a formulation that makes it possible to decouple the dynamics at topology change. A key point is an eigenvalue problem that characterizes several aspects of energy and momentum transfer at the discontinuous topology transition.