Applying KAM Theory to Highly Eccentric Orbits

Abstract

This research applies KAM theory to highly eccentric orbits for earth orbiting satellites by using spectral methods to nd the three basis frequencies resulting from earth's geopotential. Once a torus is created from these frequencies, its dynamics data can be compared to the position data of an integrated data set over multiple orbit types, specifically, orbits with varying eccentricity. The analysis shows that many eccentric orbits are actually KAM tori when the only perturbation is the earth's geopotential. The residuals agree to 10s of meters in most cases. This research also outlines many of the limitations of the current method and gives recommendations for further study and real-world applications. Applications focus on space debris and non-operational satellites.

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Document Details

Document Type
Technical Report
Publication Date
Mar 27, 2014
Accession Number
ADA599791

Entities

People

  • Adam B. Dunk

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Air Force
  • Artificial Satellites
  • Astronautics
  • Computational Science
  • Elliptical Orbits
  • Frequency
  • Global Positioning Systems
  • Low Earth Orbits
  • Molecular Mechanics Methods
  • N Body Problem
  • Orbital Elements
  • Orbital Mechanics
  • Orbits
  • Perturbation Theory
  • Satellite Orbits
  • Space Debris
  • Spacecraft Orbits

Readers

  • Riverine Ecology
  • Space Exploration and Orbital Mechanics.
  • Systems Analysis and Design

Technology Areas

  • Space
  • Space - Orbital Debris