Plane periodic satellite motions relative to center of mass in neighborhood of collinear libration point

Details Plane periodic satellite motions relative to center of mass in neighborhood of collinear libration point Plane periodic satellite motions relative to center of mass in neighborhood of collinear libration point

Feb 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988rpsct...3...15c&link_type=abstract

In its JPRS Report: Science and Technology. USSR: Space p 15 (SEE N88-30498 24-88) Transl. into ENGLISH from Kosmicheskiye Issle

Computer Science

Libration, Orbital Mechanics, Periodic Variations, Satellite Orbits, Center Of Mass, Coordinates, Liapunov Functions, Trajectory Analysis

Scientific paper

By applying the Lyapunov theorem on a holomorphic integral it can be demonstrated that there are two families of periodic motions of a point of infinitely small mass near the libration point L2. A study was made of one of these families of periodic motions for which the center of satellite mass moves in an orbit lying in the plane of motion of finite masses m1 and m2, the distance between which is used as a unit of length. Such motion is possible with ordinary assumptions concerning the nondependence of the trajectory of the satellite center of mass on its motion relative to the center of mass. Three right-handed coordinate systems are introduced for solution of the problem. The extent of the periodic orbit of satellite center of mass near L2 is considered small in comparison with the distance between the m1 and m2 points, characterized by the small parameter gy. This orbit can be stipulated by series in powers of gy. The equations of satellite motion relative to its center of mass allow solutions corresponding to plane motions for which one of the main central axes of the ellipsoid of satellite inertia during the entire time of motion is perpendicular to the orbital plane. With this taken into account, a study is made of the problem of existence and stability of periodic motions produced by plane rotations and oscillations of an arbitrary amplitude.

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