Astronomy and Astrophysics – Astronomy
Scientific paper
Mar 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..94..317s&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 94, Issue 3, pp.317-349
Astronomy and Astrophysics
Astronomy
13
Scientific paper
Equilibrium conditions for a mutually attracting general mass distribution and point mass are derived and their stability computed. The equilibrium conditions can be reduced to six equations in six unknowns, plus the existence of four integrals of motion consisting of the total angular momentum and energy of the system. The equilibrium conditions are further reduced to two independent equations, and their theoretical properties are studied. We derive three distinct conditions for a relative equilibrium which can be used to derive robust algorithms for solving these problems for non-symmetric gravity fields: a set of necessary conditions, a set of sufficient conditions, and a set of necessary and sufficient conditions. Each of these conditions is well suited for the computation of certain classes of equilibria. These equations are solved for non-symmetric gravity fields of interest, using a real asteroid shape model for the general gravity fields. Explicit conditions for the spectral and energetic stability of the resulting equilibria are also derived and computed for the shape of interest.
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