Abstract
Letx 0 (t),x 0 ɛℝ4 be a homothetic solution of the planar three-body problem with total energyh, described in relative coordinates with respect to one body. It is shown that the variational equation of the problem atx 0 (t) can be solved explicitly in terms of hypergeometric functions. This is done by using the scaled true anomaly of the one-dimensional Kepler motion as the independent variable.
The classical theorems about hypergeometric functions allow a simple calculation of all the values needed in applications. By means of this theory the past of a homothetic triple close encounter may be described in a linearized approximation.
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Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.
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Waldvogel, J. The variational equation of the three-body problem. Celestial Mechanics 21, 171–175 (1980). https://doi.org/10.1007/BF01230894
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DOI: https://doi.org/10.1007/BF01230894