2016/05/06 by D. J. Scheeres
Engineering · Mathematics · Physics and Astronomy · #Angular momentum #Astro and Planetary Science #Bifurcation #Constant (computer programming) #Finite set #Moment (physics) #Pulsars and Gravitational Waves Research #Relative density #Spacecraft Dynamics and Control #Stability (learning theory) #astro-ph.EP #math.DS #physics.class-ph
paper · pdf · doi:10.1007/s00332-016-9309-6
Accepted for publication in the Journal of Nonlinear Science
arxiv created 2016/05/06 · openalex publication_date 2016/05/26 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The relative equilibria for the spherical, finite density three-body problem are identified. Specifically, there are 28 distinct relative equilibria in this problem which include the classical five relative equilibria for the point-mass three-body problem. None of the identified relative equilibria exist or are stable over all values of angular momentum. The stability and bifurcation pathways of these relative equilibria are mapped out as the angular momentum of the system is increased. This is done under the assumption that they have equal and constant densities and that the entire system rotates about its maximum moment of inertia. The transition to finite density greatly increases the number of relative equilibria in the three-body problem and ensures that minimum energy configurations exist for all values of angular momentum.