The authors introduce an electromagnetic curvature criterion for linear stability of relative equilibria in the planar n-body problem, recovering Routh's criterion for three bodies and providing an instability test when dynamics split into symplectic planes.
On the role of bifurcation theory and curvature in the existence and stability of periodic orbits in electromagnetic systems and then-body problem.Dissertation
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Relative equilibria, linear stability and electromagnetic curvature
The authors introduce an electromagnetic curvature criterion for linear stability of relative equilibria in the planar n-body problem, recovering Routh's criterion for three bodies and providing an instability test when dynamics split into symplectic planes.