  We provide conditions under which trajectory outcomes in mechanical systems
subject to unilateral constraints depend piecewise-differentiably on initial
conditions, even as the sequence of constraint activations and deactivations
varies. This builds on prior work that provided conditions ensuring existence,
uniqueness, and continuity of trajectory outcomes, and extends previous
differentiability results that applied only to fixed constraint (de)activation
sequences. We discuss extensions of our result and implications for assessing
stability and controllability.
