Elimination of a coordinate singularity in the three-body problem

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Abstract
One of the coordinate systems commonly used in the three-body problem consists of three center-of-mass coordinates, three interparticle separations, and three Euler angles specifying the orientation of the triangle whose vertices are the three particles. The usual specification of the Euler angles for this system, which aligns the axes of the body-fixed coordinate system with the principal axes of the moment of inertia tensor, results in a coordinate singularity whenever two of the moments of inertia are equal. An alternative specification of the Euler angles for the equal mass case which treats the three particles symmetrically and eliminates the coordinate singularity at the equilateral triangle configuration is presented.