**DDA 36th Meeting, 10-14 April 2005**

*Session 13 The Quest for Precision*

Oral, Wednesday, April 13, 2005, 3:05-5:45pm
Previous |
Session 13 |
Next

## [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.

If you would like more information about this abstract, please
follow the link to http://arnold.usno.navy.mil/murison/Genie/.
This link was provided by the
author. When you follow it, you will leave the Web site for this
meeting; to return, you should use the Back comand on your
browser.

Previous |
Session 13 |
Next

Bulletin of the American Astronomical Society, **37** #2

© 2005. The American Astronomical Soceity.