Equilibrium forms of flexible tether in the plane of circular orbit. 0- and 1-parametric families

Equilibrium forms in the orbital frame of a flexible inextendible tether moving in the plane of circular orbit are considered. Gravity-gradient, aerodynamical, electromagnetic and inertial forces are taken into account. The problem does not include equilibria conditions of the whole system, which must be satisfied by the corresponding choice of the tether tension forces upon its ends. Analysis of symmetries of the equation system which describes the equilibrium tether forms made it possible to diminish the investigated set of the curves. It was shown particularly that if gravity-gradient force may be ignored then there exists for given forces only finite set of essentially different equilibrium forms of the tether (which cannot be reduced to each other by similarity transformations and translations). The possibility of analitic description of the equilibrium forms was explored. Detailed analysis of the forms was performed in 11 cases with incomplete set of force factors.