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Modelling Very-High-Eccentricity Asteroidal Librations with the Andoyer Hamiltonian

Published online by Cambridge University Press:  12 April 2016

A. Simula ,
S. Ferraz-Mello  and
C. Giordano
A. Simula
Affiliation:
Instituto Astronômico e Geofísico. Universidade de São Paulo Av. Miguel Stéfano 4200, São Paulo, SP, Brazil
S. Ferraz-Mello
Affiliation:
Instituto Astronômico e Geofísico. Universidade de São Paulo Av. Miguel Stéfano 4200, São Paulo, SP, Brazil
C. Giordano
Affiliation:
Universid Nacional de La Plata- La Plata, Argentina

Extract

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High-eccentricity asteroidal librations are modelled using the high-eccentricity non-planar asymmetric expansion (Roig et al 1997). This second-degree expansion gives us the potential of the perturbing forces acting on a resonant asteroid in a first order resonance in explicit form, as a quadratic polynomial in the canonical non-singular variables. Secular and short periodic perturbations are introduced in the model, giving a more realistic description of the dynamics.

The reducing Sessin’s transformation (Sessin, 1981; Sessin & Ferraz-Mello, 1984) is used to include the main effect of Jupiter’s ecc entricity in the main part of the Hamiltonian. It leads to an integrable first-order approximation known as the second fundamental model for resonance (Henrard & Lemaitre 1983) or Andoyer Hamiltonian (Andoyer 1903).

Type
Extended Abstracts
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 389 - 390
Copyright
Copyright © Kluwer 1999

References

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