Spatial equilibria of multibody chain in a circular orbit

We study spatial equilibria of a multibody connected system within the framework of the model of n+1n+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.