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Integration theory for the restricted problem of three axisymmetric bodies

โœ Scribed by S. M. El-Shaboury

Publisher
Springer Netherlands
Year
1990
Tongue
English
Weight
332 KB
Volume
48
Category
Article
ISSN
1573-0794

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โœฆ Synopsis

In this paper the circular planar restricted problem of three axisymmetric ellipsoids S,(i = 1,2,3), such that their equatorial planes coincide with the orbital plane of the three centres of masses. be considered. The equations of motion of infinitesimal body Sa be obtained in the polar coordmates.

Using iteration approach we have given an approximation for another integral, which independent of the Jacobian integral, in the case of P-type orbits (near circular orbits surrounding both primaries).

๐Ÿ“œ SIMILAR VOLUMES

The equilibrium solutions of restricted
The equilibrium solutions of restricted problem of three axisymmetric rigid bodies
โœ S. M. Elshaboury ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 272 KB

In this paper we consider the restricted problem of three axisymmetric rigid bodies under the central forces. The collinear and triangular equilibrium solutions are obtained. Finally a numerical study of the influence of the non-sphericity and the rotation of the primaries in the location of the lib

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## Abstract The algorithm for constructing the first integrals of motion of the regularized restricted planar problem of three bodies is proposed. The integrals are constructed as the formal power series in one from variables. It is shown that coefficients of these series are trigonometric polynomi

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โœ S. M. El-Shaboury ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 311 KB

The restricted problem of 2 + 2 homogenous axisymmetric ellipsoids such that their equatorial planes coincide with the orbital plane of the centers of mass is considered. The equilibrium solutions of this problem are shown to exist. Six of these solutions are located about the collinear points of th