The stability of linear multi-degree-of-freedom stable potential systems with multiple natural frequencies under the action of infinitesimal circulatory forces is considered. Contrary to the received view that such systems are inherently unstable, a careful study shows that such systems have a much more complex behaviour than previously recognized and could exhibit an alternation of stability and instability that depends on the structure of the potential system and its interaction with the circulatory forces. The conditions under which stability or instability ensues and the nature of this alternation in stability are explicitly obtained. In low-dimensional stable potential systems, when the coefficients of the circulatory forces are proportional to an arbitrarily small scalar parameter, all the circulatory forces that cause flutter instability are described.

考虑了在无限小循环力作用下具有多个固有频率的线性多自由度稳定势系统的稳定性。与已收到的关于此类系统天生不稳定的观点相反，一项仔细的研究表明，此类系统的行为比以前公认的复杂得多，并且可能表现出取决于潜在系统的结构及其与之交互作用的稳定性和不稳定性的交替。循环力。明确获得了发生稳定性或不稳定性的条件以及这种稳定性变化的性质。在低维稳定势系统中，当循环力的系数与任意小的标量参数成比例时，