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The paper investigates the stability of a linear mechanical system subjected to potential and circulatory forces. Three theorems which provide stability conditions directly in terms of the coefficient matrices are established.Mathematics Subject Classification (1991). 70J25.

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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 to those obtained earlier.

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