Mathematics
Scientific paper
Mar 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983baicz..34...65s&link_type=abstract
Astronomical Institutes of Czechoslovakia, Bulletin (ISSN 0004-6248), vol. 34, March 1983, p. 65-74.
Mathematics
9
Hamiltonian Functions, Orbital Mechanics, Rigid Structures, Three Body Problem, Transformations (Mathematics), Rotation, Spherical Harmonics
Scientific paper
Andoyer variables for rotation and Delaunay variables based on Jacobi coordinates for orbital motion are used to formulate the three rigid body problem in suitable canonical variables. Knowledge of the density distribution inside the bodies is not required and only their Stokes constant must be known. The Hamiltonian of the problem is presented without truncation of the relevant Fourier series. Averaging is performed over the fast variablaes assuming no commensurability. The general Hamiltonian is obtained by employing the transformation properties of the spherical harmonics in terms of transformation matrices. For some special cases the first terms are explicitly given.
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