Three-body relative equilibria on S² II: Extended Lagrangian configurations

2022/02/21 by Fujiwara, Toshiaki, Perez-Chavela, Ernesto
#70F07 #70F15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.12708

Abstract

This is a natural continuation of our first paper \citepre, where we develop a new geometrical technique which allow us to study relative equilibria on the two sphere. We consider a system of three positive masses on \mathbbS² moving under the influence of an generic attractive potential which only depends on the mutual distances among the masses. We reduce the problem of finding extended Lagrangian relative equilibria to the analysis of the inertia tensor, then we obtain a more manageable equivalent inertia tensor which allow us to find new families of Lagrangian configurations.

Related

• Three-body relative equilibria on \mathbbS² I: Euler configurations
• A new method to study relative equilibria on \mathbbS²
• Three body relative equilibria on \mathbbS²
• Mass independent shapes for relative equilibria in the two dimensional constant positive curved three body problem
• Continuations and bifurcations of relative equilibria for the positive curved three body problem