DDA 36th Meeting, 10-14 April 2005
Session 13 The Quest for Precision
Oral, Wednesday, April 13, 2005, 3:05-5:45pm

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[13.04 (title only)] A Genetic Algorithm Approach to Finding Orbit-Orbit Distance Function Stationary Points

M.A. Murison (USNO)

In its most-reduced form, the function F describing the squared distance between two points lying on confocal elliptical orbits has six free parameters (semimajor axes ratio, orbital eccentricities, and relative inclination, node, and pericenter) in addition to the two independent variables (true or eccentric anomalies). Thus, F defines a family of two-dimensional differentiable manifolds. The extrema of a surface specified by a particular set of parameter values may be found by setting the derivatives of F equal to zero, which will additionally identify the saddle points. The maximum number of stationary points for this problem is currently unknown, though Gronchi (2001) was able to extablish an analytical upper bound of 16 by use of a theorem from algebraic geometry by Bernstein (1975). It would seem that exploring the six-dimensional parameter space numerically would be prohibitively expensive. However, this problem is suitable for numerical exploration by means of genetic algorithms. This paper reports preliminary results from application of genetic algorithms to searching for the maximum number of stationary points of F.

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Bulletin of the American Astronomical Society, 37 #2
© 2005. The American Astronomical Soceity.