Stability of Dynamical Systems with Circulatory Forces: Generalization of the Merkin Theorem

Abstract

This paper develops a general result on the stability of undamped linear multi-degree-of-freedom systems that are subjected to potential and circulatory forces. The result is a generalization of Merkin’s celebrated result on flutter instability in stable potential systems that are subjected to circulatory disturbances. Merkin’s result appears as a special case of the generalization obtained herein.