A mechanical system under strongly nonlinear potential and dissipative forces, with nonlinear nonstationary perturbations having zero mean values, is studied. Proposing a special construction of Lyapunov function, the conditions are found, under which the perturbations do not influence the asymptotic stability of the trivial equilibrium position of the system. These conditions include the requirements on asymptotic stability of the disturbance-free system and the relations of the nonlinearity orders between potential and dissipative forces. The developed approach is extended to the problem of monoaxial stabilization of a rigid body.

中文翻译：

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强非线性机械系统稳定性分析的平均方法

研究了在强非线性势和耗散力作用下，非线性非平稳扰动均值为零的机械系统。提出了一种特殊的Lyapunov函数构造，找到了扰动不影响系统平凡平衡位置渐近稳定性的条件。这些条件包括无扰动系统对渐近稳定性的要求以及势能和耗散力之间的非线性阶数关系。所开发的方法扩展到刚体的单轴稳定问题。