Centroid-Referenced Admissibility in Constrained Dynamics

This paper introduces a centroid-referenced admissibility framework for constrained dynamical systems. By expressing system evolution relative to an intrinsic centroid datum rather than an external coordinate origin, admissibility can be evaluated as deviation from internal equilibrium. Constraints are represented as measurable fields with tolerance bounds, yielding a scalar admissibility margin that determines whether continuation is permitted. A local directional admissibility set is defined, characterizing allowable infinitesimal motions. It is shown that tightening constraints causes admissible direction sets to shrink monotonically and potentially collapse to the empty set, producing a well-defined no-go condition. The formulation is consistent with classical stability and feasibility methods while providing a unified geometric representation.