On the Generalization of Merkin’s Theorem for Circulatory Systems: A Rank Criterion

Abstract

This paper provides a generalization of the celebrated Merkin theorem. It provides new results on the destabilizing effect of circulatory forces on stable potential systems. Previous results are described and discussed, and the paper uncovers a deeper understanding of the fundamental reason for the destabilization. Instability results in terms of rank conditions that deal with the potential and circulatory matrices that describe the system are obtained, thereby generalizing this remarkable theorem. These new results are compared with those obtained earlier.