Solutions of singular constrained differential equations: A generalization of circuits containing capacitor-only loops and inductor-only cutsets

Employing the theory of differentiable manifolds we give a geometric coordinate-free description of constrained differential equations (CDE), which are usually thought of as systems of simultaneous differential and algebraic equations. We regard the algebraic constraints as defining a differentiable manifold, , and regard solutions of the CDE as curves in . Our main contribution in this paper is to characterize geometrically a particular class of singular constrained differential equations for which consistency forces solutions to lie in a proper subset of . Constrained differential equations describing electric circuits having capacitor-only loops and/or inductor-only cutsets are shown to be of the above type.