Deprit's reduction of the nodes revisited

Luigi Chierchia (1) , Gabriella Pinzari (2)

1 Dipartimento di Matematica
2 Dipartimento di Matematica ed Applicazioni "R. Caccioppoli"

We revisit a set of symplectic variables introduced by Andre Deprit (Celest Mech , 181-195, 1983), which allows for a complete symplectic reduction in rotation invariant Hamiltonian systems, generalizing to arbitrary dimension Jacobi's reduction of the nodes. In particular, we introduce an action-angle version of Deprit's variables, connected to the Delaunay variables, and give a new hierarchical proof of the symplectic character of Deprit's variables.

Mots clés: Symplectic coordinates; Action-angle variables; Deprit reduction of the nodes; -body problem; Planetary system

Luigi Chierchia, Gabriella Pinzari. Deprit's reduction of the nodes revisited. Celestial Mechanics and Dynamical Astronomy, 2011, 109 (3), pp.285-301. ⟨10.1007/s10569-010-9329-8⟩. ⟨hal-00609755⟩