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.
On certain M\"obius type solutions for the n-body problem in a positive space form
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abstract
We study here the Mobius type solutions for the n-body problem in a two dimensional positive space form M^2_R. With methods of Mobius geometry and using the Iwasawa decomposition of the Mobius group of automorphisms Mob_2 (M^2_R), we state algebraic functional conditions for the existence of such type of solutions in M^2_R. We mention some examples of these type of solutions.
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physics.class-ph 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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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.