Piecewise-differentiable trajectory outcomes in mechanical systems subject to unilateral constraints
This provides a theoretical foundation for assessing stability and controllability in mechanical systems with constraints, but it is incremental as it extends previous differentiability results.
The paper tackles the problem of how trajectory outcomes in mechanical systems with unilateral constraints depend on initial conditions, showing they are piecewise-differentiable even as constraint activation sequences vary, building on prior work that established existence, uniqueness, and continuity.
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.