Abstract
We develop a method for studying the curvature of the configuration space of a dynamical system equipped with the Maupertuis metric, for a given value of the energy constant, using the symbolic manipulation program Macsyma. We apply this method in the planar three-body problem. Discussion of the sign of the Riemann curvatures enables one to study the stability of particular configurations. For Lagrange's homothetic triangular solution, we found conditions when all the Riemann curvatures are negative. This means that under these conditions, the homothetic Lagrange solution is exponentially unstable.
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Schedule a callMore From: Comptes Rendus de l'Academie des Sciences Series IIB Mechanics Physics Astronomy
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