Abstract

Small transverse oscillations near the equilibrium vertical position are studied for an extra-long flexible inextensible cable of a space elevator. The linear approximation shows that the oscillations in the two planes, equatorial and meridional, are separated and have identical sets of eigenfunctions, while their eigenfrequencies are connected by a simple relation. A Sturm–Liouville problem for determining the frequencies and modes of the cable’s natural oscillations is stated. A transformation of the problem aimed at simplifying computations is described.

中文翻译：

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空间电梯电缆的线性横向振荡

摘要

研究了太空升降机的超长挠性，不可伸长电缆在平衡垂直位置附近的小横向振动。线性近似表明，在赤道和子午两个平面上的振动是分开的，并且具有相同的本征函数集，而它们的本征频率通过简单的关系连接。提出了用于确定电缆自然振荡的频率和模式的Sturm-Liouville问题。描述了旨在简化计算的问题的变换。