This paper addresses the problem of stability of equilibria of mechanical systems in nonpotential force fields. In the linear approximation, any nonpotential force is uniquely represented as the sum of a potential force and a circulatory force. The instability of equilibrium is established for the nonlinear problem in the case when the linearized system has a pair of zero eigenvalues. The mechanism of stability loss is due to the appearance of two asymptotic trajectories, one that enters an equilibrium point and one that exits it. A similar result takes place when additional gyroscopic forces and viscous friction forces are taken into account. Asymptotic solutions can be obtained in the form of series in inverse powers of time whose coefficients are polynomials in logarithms of time.

本文解决了非势力场中机械系统平衡的稳定性问题。在线性近似中，任何非势力都唯一地表示为势力和循环力的总和。当线性化系统具有一对零特征值时，针对非线性问题建立了平衡的不稳定性。稳定性损失的机制是由于两条渐近轨迹的出现，一条进入平衡点，一条退出平衡点。当考虑额外的陀螺力和粘性摩擦力时，会出现类似的结果。渐近解可以以时间的逆幂级数的形式获得，其系数是时间对数的多项式。