Abstract—

A system with two degrees of freedom in the case of a double natural frequency is considered. The unperturbed system consists of two independent oscillators. The system coordinates describe an elliptical trajectory with four orbital elements. An analysis of the action of linear perturbations (forces) on the orbital elements is carried out. Perturbations are subdivided into six types of forces, and for each type of forces a system of differential equations for the orbital elements is obtained. For all six types of forces, a general solution of the system of differential equations in elementary functions is found.

中文翻译：

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具有两个自由度的线性共振系统的摄动作用分析

摘要-

考虑在双固有频率的情况下具有两个自由度的系统。不受干扰的系统由两个独立的振荡器组成。系统坐标描述了具有四个轨道元素的椭圆轨迹。对线性扰动（力）对轨道元件的作用进行了分析。摄动细分为六种力，对于每种力，都获得了轨道元素的微分方程组。对于所有六种力，都找到了基本函数中的微分方程组的一般解。