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.
Lectures on the free period Lagrangian action functional.J
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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.