An analytical method for out-of-plane relative equilibrium formation using inter-spacecraft forces

For out-of-plane relative equilibrium of a two-spacecraft formation achieved by internal forces, this paper proposes a scheme which complies with the characteristics of angular momentum conservation to analyze such a formation over the entire parameter space. By purposely rewriting one of the equilibrium condition, this paper defines a modification of the set of equations for the out-of-plane equilibrium configurations. Thereby, the relative equilibrium can be solved analytically in the whole multidimensional real number field through these equations. Numerical examples are also included to provide some insight about the equilibrium conditions. Moreover, the results from derivation and illustrative examples disclose a novel picture of the out-of-plane relative equilibrium.