Collinear Equilibrium Solutions of Four-body Problem

We discuss the equilibrium solutions of four different types
of collinear four-body problems having two pairs of equal masses. Two of these four-body models are symmetric about the center-of-mass while the other two are non-symmetric.We define two mass ratios as μ1 = m1/MT and μ2 = m2/MT, where m1 and m2 are the two unequal masses and MT is the total mass of the system. We discuss the existence of continuous
family of equilibrium solutions for all the four types of four-body problems.