Kron's method: A consequence of the minimization of the primitive lagrangian in the presence of displacement constraints

Abstract

A method whereby the Kron eigenvalue procedure can be deduced from the classical process of minimizing a Lagrangian subject to displacement constraints is presented. A new “dual” formulation of Kron's method is also given—this offering the advantages of a smaller frequency determinant in certain instances. Both techniques are illustrated in relation to simple mass-spring systems, although these techniques are most useful when dealing with systems of very large dimensionality.