Periodic solutions about the collinear lagrangian solution in the general problem of three bodies |
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| Authors: | R. Broucke J. D. Anderson L. Blitzer E. Davoust H. Lass |
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| Affiliation: | (1) Department of Aerospace Engineering and Engineering Mechanics, University of Texas, 78712 Austin, Texas, USA;(2) Jet Propulsion Laboratory, 91103 Pasadena, California, USA;(3) Department of Physics, University of Arizona, 85721 Tucson, Arizona, USA;(4) Department of Astronomy, University of Texas, 78712 Austin, Texas, USA;(5) Jet Propulsion Laboratory, 91103 Pasadena, California, USA;(6) Present address: Observatoire de Besançon, Besançon, France |
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| Abstract: | The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame.The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses.Finally, the fundamental family of periodic solutions is extended by numerical integration all the wap up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated. |
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