16-50 Gabriella Pinzari

A first integral to the partially averaged Newtonian potential of the three--body problem (708K, PDF) Jul 10, 16

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Abstract. We consider the partial average exttt{i.e.}, the Lagrange average with respect to {\it just one} of the two mean anomalies, of the Newtonian part of the perturbing function in the three--body problem Hamiltonian. We prove that such a partial average exhibits a non--trivial first integral. We next show how this integral is responsible of three known occurrences in the averaged Newtonian potential: Harrington property, Herman resonance and certain strange symmetries in the planetary torsion.

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