Abstract—

A mechanical system with two rotational degrees of freedom is considered. The mathematical model is presented in the form of a fourth-order dynamic system. A numerical–analytical iterative method is proposed for finding solutions close to periodic, corresponding to the autorotation modes of a mechanical system. Fixed points (including saddles) of the system averaged over two angles are used as a zero approximation. At each iteration, periodic solutions of two auxiliary subsystems are numerically constructed using an approach akin to the Andronov–Pontryagin method. Under the condition of the convergence of the method, a set of periodic functions is obtained, which presumably approximately describe trajectories close to periodic, in particular, quasiperiodic. The conditions for the applicability of the approach are discussed. The proposed method is illustrated by the example of finding the autorotation modes of two interacting Savonius rotors.

中文翻译：

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搜索具有两个旋转自由度的机械系统的自转数的数值分析方法

摘要-

考虑具有两个旋转自由度的机械系统。数学模型以四阶动态系统的形式呈现。提出了一种数值分析迭代方法来寻找接近周期性的解，对应于机械系统的自转模式。系统的固定点（包括鞍点）在两个角度上平均用作零近似值。在每次迭代中，使用类似于 Andronov-Pontryagin 方法的方法在数值上构建两个辅助子系统的周期解。在该方法收敛的条件下，得到了一组周期函数，大概可以近似描述接近周期，特别是准周期的轨迹。讨论了该方法的适用条件。