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On the stability of the solutions of the general problem of three bodiesThe extent through which the initial conditions of a given three-body system may be varied without completely changing the qualitative nature of the subsequent system evolution is investigated. It is assumed that the three masses are equal, all initial velocities are zero, the first two bodies initially lie on the x-axis, and the position of the third body is confined to a specific region of space. Analysis of the system evolution for different initial positions of the third body shows that there is a whole area or 'island' in the x-y plane throughout which the initial position of the third body may be moved in a continuous fashion to produce an evolution which also changes in a continuous manner. A Monte Carlo approach is adopted to determine the full extent of this island in the general problem. It is concluded that the stability of a full solution may be directly related to the size of its island in phase space.
Document ID
19770050730
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Standish, E. M., Jr.
(California Institute of Technology, Jet Propulsion Laboratory, Pasadena Calif., United States)
Date Acquired
August 9, 2013
Publication Date
December 1, 1976
Publication Information
Publication: Celestial Mechanics
Volume: 14
Subject Category
Astronomy
Accession Number
77A33582
Distribution Limits
Public
Copyright
Other

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