Using a new cot(theta/2) potential, the authors show that antipodal configurations on the sphere arise as limits of isosceles relative equilibria and satisfy a regularized equation of motion.
Reduction and relative equilibria for the two-Body on spaces of constant curvature
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Conjugated equilibrium solutions for the $2$--body problem in the two dimensional sphere $\mathbb{M}^2_R$ for equal masses
Using a new cot(theta/2) potential, the authors show that antipodal configurations on the sphere arise as limits of isosceles relative equilibria and satisfy a regularized equation of motion.