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Periodic solutions about the collinear Lagrangian solution in the general problem of three bodiesThe 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 way up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.
Document ID
19810049056
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Broucke, R.
(Texas Univ. Austin, TX, United States)
Davoust, E.
(Texas, University Austin, Tex., United States)
Anderson, J. D.
(Texas Univ. Austin, TX, United States)
Lass, H.
(California Institute of Technology, Jet Propulsion Laboratory, Pasadena Calif., United States)
Blitzer, L.
(Arizona, University Tucson, Ariz., United States)
Date Acquired
August 11, 2013
Publication Date
May 1, 1981
Publication Information
Publication: Celestial Mechanics
Volume: 24
Subject Category
Astronomy
Accession Number
81A33460
Funding Number(s)
CONTRACT_GRANT: NAS7-100
Distribution Limits
Public
Copyright
Other

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