On the double averaged three-body problem |
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| Authors: | M Šidlichovskyý |
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| Institution: | 1. Astronomical Institute of the Czechoslovak Academy of Sciences, Budecská 6, 120 23, Praha 2, Czechoslovakia
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| Abstract: | The Hamiltonian of three point masses is averaged over fast variablel and ll (mean anomalies) The problem is non-planar and it is assumed that two of the bodies form a close pair (stellar three-body problem). Only terms up to the order of (a/á)4 are taken into account in the Hamiltonian, wherea andá are the corresponding semi-major axes. Employing the method of elimination of the nodes, the problem may be reduced to one degree of freedom. Assuming in addition that the angular momentum of the close binary is much smaller than the angular momentum of the motion of the binary around a third body, we were able to solve the equation for the eccentricity changes in terms of the Jacobian elliptic functions. |
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