Effective Hamiltonian for the D'Alembert Planetary Model Near a Spin/Orbit Resonance

Details Effective Hamiltonian for the D'Alembert Planetary Model Near a Spin/Orbit Resonance Effective Hamiltonian for the D'Alembert Planetary Model Near a Spin/Orbit Resonance

May 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002cemda..83..223b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 83, Issue 1, p. 223-237 (2002).

Astronomy and Astrophysics

Astronomy

2

Hamiltonian Systems, D'Alembert Model, Spin/Orbit Resonances, Fast Averaging, Nekhoroshev Normal Forms, Proper Degeneracies, Stability, Effective Hamiltonian

Scientific paper

The D'Alembert model for the spin/orbit problem in celestial mechanics is considered. Using a Hamiltonian formalism, it is shown that in a small neighborhood of a p:q spin/orbit resonance with (p,q) different from (1,1) and (2,1) the `effective' D'Alembert Hamiltonian is a completely integrable system with phase space foliated by maximal invariant curves; instead, in a small neighborhood of a p:q spin/orbit resonance with (p,q) equal to (1,1) or (2,1) the `effective' D'Alembert Hamiltonian has a phase portrait similar to that of the standard pendulum (elliptic and hyperbolic equilibria, separatrices, invariant curves of different homotopy). A fast averaging with respect to the `mean anomaly' is also performed (by means of Nekhoroshev techniques) showing that, up to exponentially small terms, the resonant D'Alembert Hamiltonian is described by a two-degrees-of-freedom, properly degenerate Hamiltonian having the lowest order terms corresponding to the `effective' Hamiltonian mentioned above.

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