# A first integral to the partially averaged Newtonian potential in the three-body problem

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Gabriella Pinzari
(Università di Napoli "Federico II")

created by paolini on 19 Oct 2016

25 oct 2016
-- 16:00
[open in google calendar]

Aula dal Passo - Universita' degli Studi di Roma "Tor Vergata"

SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Universita' degli Studi di Roma "Tor Vergata"

**Abstract.**

We consider the partial average, i.e., the Lagrange average with
respect to *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.