Abstract

This study is a continuation of the article “Optimization of oscillation damping modes of a spatial double pendulum: 1. Formulation of the problem,” in which the problem of the optimal oscillation damping of a double pendulum with hinged noncollinear axes was formulated. Passive damping (viscous friction) is considered separately, and the possibility of additional account of active impacts (collinear control) is also explored. Two optimization criteria are introduced that characterize the efficiency of the damping of system motion: first, the degree of stability is maximized, and then the integral energy-time criterion is minimized. The optimal values of the parameters of the damping variants under consideration are determined by applying both criteria in finding the exact solution of the problem in a linear model. The results obtained are presented as visual graphic illustrations which enable determination of their main qualitative and quantitative features. The conclusions made can be useful in studying the motions of manipulators and various robotic structures.

中文翻译：

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空间双摆振动阻尼模态优化：二、问题求解及结果分析

摘要

这项研究是文章“空间双摆的振荡阻尼模式的优化：1. 问题的表述”一文的延续，其中阐述了具有铰链非共线轴的双摆的最佳振荡阻尼问题。被动阻尼（粘性摩擦）被单独考虑，并且还探讨了额外考虑主动影响（共线控制）的可能性。引入了两个表征系统运动阻尼效率的优化准则：首先，稳定度最大化，然后积分能量-时间准则最小化。所考虑的阻尼变体的参数的最佳值是通过应用这两个标准来确定的，以在线性模型中找到问题的精确解。获得的结果以视觉图形说明的形式呈现，可以确定其主要的定性和定量特征。得出的结论可用于研究机械手和各种机器人结构的运动。