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Interpretation of Floquet Eigenvalues and Eigenvectors for Periodic Systems

机译:周期系统的浮点特征值和特征向量的解释

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The application of Floquet analysis to rotorcraft has demonstrated that there is often misunderstanding as to how to interpret the integer-multiple arbitrariness in the imaginary part of the characteristic exponents of the system (i.e., in the frequency). Although some papers have offered various methodologies for choosing the "correct" frequency (such as choice of the strongest harmonic in the periodic eigenvector), confusion still persist and none of the proposed methods completely solves the difficulty. The purpose of this present paper is to (1) offer a history of analysis of periodic systems with respect to the treatment of the integer multiples, (2) propose a practical tool for fundamental insight into system frequencies, and (3) show demonstratively for simple cases why no single integer can adequately describe system dynamics. It is hoped that this approach will provide clarity to a problem that, although long understood in principle, still leads to confusion in published papers.
机译:Floquet分析在旋翼飞机上的应用表明,在系统特征指数的虚部(即频率)中,如何解释整数任意性经常引起误解。尽管一些论文提供了多种选择“正确”频率的方法(例如,选择周期性特征向量中最强的谐波),但仍然存在混淆,并且所提出的方法都无法完全解决这一难题。本文的目的是(1)提供关于整数倍数处理的周期系统分析的历史,(2)提出用于深入了解系统频率的实用工具,以及(3)证明对于为什么没有单个整数可以充分描述系统动力学的简单情况。希望这种方法可以澄清一个问题,尽管该问题在原则上早已理解,但仍然导致已发表论文的混乱。

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