Stationary motions in a restricted problem of three rigid bodies

Details Stationary motions in a restricted problem of three rigid bodies Stationary motions in a restricted problem of three rigid bodies

Dec 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31..339e&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 31, Dec. 1983, p. 339-362.

Physics

5

Axisymmetric Bodies, Circular Orbits, Motion Stability, Orbital Mechanics, Three Body Problem, Euler-Lagrange Equation, Rigid Structures

Scientific paper

The present paper is a continuation of papers by Shinkaric (1972), Vidyakin (1976), Vidyakin (1977), and Duboshin (1978), in which the existence of particular solutions, analogues to the classic solutions of Lagrange and Euler in the circular restricted problem of three points were proved. In this paper the usage of the small-parameter method proved that in the general case the centre of mass of an axisymmetric body of infinitesimal mass does not belong to the orbital plane of the attracting bodies and is not situated in the libration points, corresponding to the classical case. Its deviation from them is proportional to the small parameter. A new type of stationary motion is found. The earlier solutions - Shinkaric (1971) and Vidyakin (1976) - are also elaborated, and stability of the stationary motions is discussed.

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