Spatial equilibria of multibody chain in a circular orbit
Spatial equilibria of multibody chain in a circular orbit
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DOI：
10.1016/j.actaastro.2005.05.002
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发表时间：
2006
影响因子：
3.5
通讯作者：
A. Guerman
中科院分区：
文献类型：
--
作者：
A. Guerman
在n个光杆(假定无质量)连接成n个链条的n+1个物质点模型的框架内，研究了多体连接系统的空间平衡。接合处是球形铰链。系统的质心沿圆形轨道运动。得到了平衡方程，并将其转化为一个相当简单的系统，方便了分析。我们对n连杆链的所有空间平衡进行了分类，证明了每个杆可以占据以下三个位置之一：它可以沿着与链质心的轨道相切的方向；它可以是位于平行于法线和双法向轨道的平面上的一组杆的成员，它是位于与轨道相切的这组杆的质心；最后，杆可以连接平行于轨道的法线和双法向平面的两组杆，或者是这样一组杆的末端，与轨道相切。作为一个例子，我们给出了四颗卫星连接成一个成员相等的三连杆链的分析，并给出了这种情况下的现有均衡方案。大多数得到的平衡实际上是二维的(虽然不一定在轨道平面上)，但我们也揭示了一些三维的四面体构型。
We study spatial equilibria of a multibody connected system within the framework of the model of n+1 material points connected by n light rods (assumed massless) into an n-link chain. The junctions are spherical hinges. The center of mass of the system moves along a circular orbit. The equilibrium equations are obtained and transformed into a rather simple system, which facilitates the analysis. We classify all the spatial equilibria of an n-link chain and prove that each rod can occupy one of the following three positions: it can be directed along the tangent to the orbit of the center of mass of the chain; it can be a member of a group of rods located in the plane parallel to the normal and bi-normal to the orbit, being the center of mass of this group situated on the tangent to the orbit; finally, the rod can either join two groups of rods parallel to plane of normal and bi-normal to the orbit, or an end of such a group with the tangent to the orbit. We include as an example the analysis of four satellites connected into a 3-link chain with equal members, and represent the schemes of existing equilibria in this case. Most of obtained equilibria are actually two-dimensional (though not necessarily lie in the orbit plane), but we also revealed a number of three-dimensional tetrahedron configurations.