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首页> 外文期刊>Cosmic research >Equilibrium Positions of a Weight on a Cable Fixed to a Dumbbell-Shaped Space Station Moving along a Circular Geocentric Orbit
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Equilibrium Positions of a Weight on a Cable Fixed to a Dumbbell-Shaped Space Station Moving along a Circular Geocentric Orbit

机译：固定在沿圆形地心轨道运动的哑铃形空间站上的电缆上的重物的平衡位置

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摘要

The motion of a space object in the gravitational field of the Earth is considered. The object consists of an extended space station and a weight, which is free to move along the cable fixed to the ends of the station. It is assumed that the station is composed of two masses coupled by a weightless rod, while the cable is weightless and non-stretched. The equations of motion of such a system are derived for the case when the motion proceeds in a single plane, while the center of mass of the system moves along a circular geocentric orbit. The conditions of the cable tension (conditions of being on tie) are derived. The phase portrait of the weight motion along the cable is constructed when the station is oriented to the attracting center or is perpendicular to this position. The possibility to leave the tie in this case is analyzed. Equilibrium configurations of the system are found, i.e., such motions of the object under consideration at which the weight does not change its position relative to the station. Lyapunov stability of such configurations is analyzed for two situations: when the station is composed of equal masses and when masses at the ends of the station are different. In particular, for the case of different masses it is established that there exist such positions of equilibrium at which the dumbbell is located at an angle to the direction to the attracting center. In some cases these positions can be stabilized (if the weight is fixed on the cable).
机译：考虑了空间物体在地球引力场中的运动。该物体包括一个扩展空间站和一个重物，该重物可沿固定在该站末端的电缆自由移动。假定该站由两个质量块组成，这些质量块由失重的杆连接，而电缆是失重的且未拉伸。当运动在单个平面中进行，而系统的质心沿着圆形的地心轨道运动时，则推导了这种系统的运动方程。得出电缆张力的条件（扎紧条件）。当工作站定向到吸引中心或垂直于此位置时，将构建沿电缆的重力运动的相图。分析了在这种情况下离开领带的可能性。找到系统的平衡配置，即，考虑中的物体的这种运动，在该运动中，重量不改变其相对于工位的位置。对于以下两种情况，分析了这种配置的Lyapunov稳定性：站点由相等质量组成时以及站点两端的质量不同时。特别地，对于不同质量的情况，确定存在这样的平衡位置，在该平衡位置处，哑铃相对于朝向吸引中心的方向成角度地定位。在某些情况下，这些位置可以稳定（如果将重物固定在电缆上）。

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