On the double averaged three-body problem

Details On the double averaged three-body problem On the double averaged three-body problem

Mar 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..29..295s&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 29, March 1983, p. 295-305.

Physics

8

Binary Stars, Celestial Mechanics, Eccentric Orbits, Elliptical Orbits, Hamiltonian Functions, Three Body Problem, Angular Momentum, Degrees Of Freedom, Earth-Moon System, Elliptic Functions, Equations Of Motion, Orbital Elements, Time Functions

Scientific paper

The Hamiltonian of three point masses is averaged over fast variable l and larcmin (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 (α/αarcmin)4 are taken into account in the Hamiltonian, α and αarcmin 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 that the angular momentum of the close binary is much smaller than the angular momentum of the motion of the binary around the third body, the author solved the equation for the eccentricity changes in terms of the Jacobian elliptic functions.

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