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Transformations of the perturbed two-body problem to unperturbed harmonic oscillatorsSingular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.
Document ID
19830053174
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Szebehely, V.
(Texas, University Austin, TX, United States)
Bond, V.
(NASA Johnson Space Center Houston, TX, United States)
Date Acquired
August 11, 2013
Publication Date
May 1, 1983
Publication Information
Publication: Celestial Mechanics
Volume: 30
ISSN: 0008-8714
Subject Category
Astronomy
Accession Number
83A34392
Distribution Limits
Public
Copyright
Other

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