用Sturm-Liouville方法求解希尔方程的稳定性图

2016 13th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE) Pub Date : 2016-09-01 DOI:10.1109/ICEEE.2016.7751252

Nestor Aguillon, J. Collado

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引用次数: 0

摘要

本文介绍了一种基于Sturm-Liouville的希尔方程稳定性图计算算法。将证明寻找Hill方程的不稳定曲线的边界可以设置为Sturm-Liouville边值问题，以及如何使用标量函数的一阶导数和二阶导数的有限差分近似将该问题设置为微分矩阵LH的特征值-特征向量问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Stability chart of Hill's equation by a Sturm-Liouville approach

This paper introduces a Sturm-Liouville based algorithm to compute the stability chart of Hill's equation. It will be shown that finding the borders of the instability tongues of Hill's equation can be set as a Sturm-Liouville boundary value problem, and how this problem can be set as an eigenvalue-eigenvector problem of a differential matrix LH using a finite-difference approximation of the first and second derivatives of a scalar function.

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2016 13th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE)

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