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Stability of Relative Equilibria in the Full Two‐Body Problem
Author(s) -
SCHEERES DJ
Publication year - 2004
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1196/annals.1311.006
Subject(s) - ellipsoid , classical mechanics , stability (learning theory) , work (physics) , spacecraft , parameterized complexity , relative motion , planar , physics , hamiltonian (control theory) , mathematics , mathematical analysis , thermodynamics , computer science , mathematical optimization , computer graphics (images) , combinatorics , astronomy , machine learning
A bstract : The stability of relative equilibrium solutions for the interaction of two massive bodies is explored. We restrict ourselves to the interaction between an ellipsoid and a sphere, both with finite mass. The study of this problem has application to modeling the relative dynamics of binary asteroids, the motion of spacecraft about small bodies, and the dynamics of gravity gradient satellites. The relative equilibrium can be parameterized by a few constants, including the mass ratio of the two bodies, the shape of the ellipsoid, and the normalized distance between the two bodies. Planar stability is characterized over this range of parameter values. When restricted to motion in the symmetry plane, the dynamical problem can be reduced to a two‐degrees of freedom Hamiltonian system, which allows for an efficient computation of stability characteristics of the relative equilibria. Future work will look at full stability of these relative equilibria.