Abstract

We consider a controlled mechanical system with one degree of freedom described by an angular coordinate. The system is under the action of conservative and nonconservative forces. It is assumed that a corresponding dynamic system has a variable parameter that describes the control-impact gain factor. An iterative numerical–analytical method designed to form autorotation modes with assigned properties is proposed. The conditions for the orbital stability of such modes are formulated. The proposed approach represents a modification of the Andronov–Pontryagin method and, as opposed to it, can be applied not only to systems close to Hamiltonian systems but also to a certain class of systems that do not contain a small parameter. An example of the method’s application to an aerodynamic pendulum model is presented. The ability to expand the method’s convergence domain by using the parameter-continuation procedure is demonstrated.

中文翻译：

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具有圆柱相空间的受控动力系统周期解的构造方法

摘要

我们考虑一个受控机械系统，该系统具有一个由角坐标描述的自由度。该制度是在保守和非保守力量的作用下进行的。假定相应的动态系统具有描述控制影响增益因子的可变参数。提出了一种迭代数值分析方法，该方法旨在形成具有指定属性的自转模式。制定了这种模式的轨道稳定性的条件。所提出的方法是对Andronov-Pontryagin方法的一种修改，并且与之相反，它不仅可以应用于接近哈密顿系统的系统，而且可以应用于不包含小参数的特定类型的系统。给出了该方法在气动摆模型中的应用示例。