Mathematics
Scientific paper
May 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..30...59s&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 30, May 1983, p. 59-69. Research supported by the University of Texas and NASA.
Mathematics
14
Harmonic Oscillators, Orbit Perturbation, Transformations (Mathematics), Two Body Problem, Equations Of Motion, Liapunov Functions, Perturbation, Radial Distribution
Scientific paper
Singular, 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.
Bond V.
Szebehely Vector
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