Linear stability of the elliptic relative equilibrium with (1 + <i>n</i> )-gon central configurations in planar n-body problem
Xijun Hu, Yiming Long, Yuwei Ou
Abstract
Abstract We study the linear stability of -gon elliptic relative equilibrium (ERE for short), that is the Kepler homographic solution with the -gon central configurations. We show that for and any eccentricity , the -gon ERE is stable when the central mass m is large enough. Some linear instability results are given when m is small.
Topics & Concepts
MathematicsEccentricity (behavior)Linear stabilityStability (learning theory)PlanarMathematical analysisInstabilityElliptic curveMarginal stabilityLinear approximationCelestial mechanicsLinear systemGeometryThree-body problemNonlinear systemSpacecraft Dynamics and ControlOptimization and Variational AnalysisAstro and Planetary Science