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Applications of ergodic theory to coverage analysis

Show simple item record Lo, Martin W. 2009-04-08T20:14:20Z 2009-04-08T20:14:20Z 2003-08-03
dc.identifier.citation AAS/AIAA Astrodynamics Specialist Conference, Big Sky, Montana, August 3-7. 2003. en_US
dc.identifier.clearanceno 03-2078
dc.description.abstract The study of differential equations, or dynamical systems in general, has two fundamentally different approaches. We are most familiar with the construction of solutions to differential equations. Another approach is to study the statistical behavior of the solutions. Ergodic Theory is one of the most developed methods to study the statistical behavior of the solutions of differential equations. In the theory of satellite orbits, the statistical behavior of the orbits is used to produce "Coverage Analysis" or how often a spacecraft is in view of a site on the ground. In this paper, we consider the use of Ergodic Theory for Coverage Analysis. This allows us to greatly simplify the computation of quantities such as the total time for which a ground station can see a satellite without ever integrating the trajectory, see Lo 1,2. More over, for any quantity which is an integrable function of the ground track, its average may be computed similarly without the integration of the trajectory. For example, the data rate for a simple telecom system is a function of the distance between the satellite and the ground station. We show that such a function may be averaged using the Ergodic Theorem. en_US
dc.description.sponsorship NASA/JPL en_US
dc.language.iso en_US en_US
dc.publisher Pasadena, CA : Jet Propulsion Laboratory, National Aeronautics and Space Administration, 2003 en_US
dc.subject Ergodic Theory en_US
dc.subject satellite orbits en_US
dc.title Applications of ergodic theory to coverage analysis en_US
dc.type Preprint en_US

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