Abstract:
We study relative equilibria (RE) for the three-body problem
on S2,
under the influence of a general potential which only depends on
cosσij where σij are the mutual angles
among the masses.
Explicit conditions for
masses mk and cosσij
to form relative equilibrium are shown.
Using the above conditions,
we study the equal masses case
under the cotangent potential.
We show the existence of
scalene, isosceles, and equilateral Euler RE, and isosceles
and equilateral Lagrange RE.
We also show that
the equilateral Euler RE on a rotating meridian
exists for general potential ∑i<jmimjU(cosσij)
with any mass ratios.
Keywords:
relative equilibria, Euler and Lagrange configurations.