The Generalized Sundman Transformation for Propagation of High-Eccentricity Elliptical Orbits

Abstract

A generalized Sundman transformation dt = crnds for exponent n 1 may be used to accelerate the numerical computation of high-eccentricity orbits, by transforming time t to a new independent variable s. Once transformed, the integration in uniform steps of s effectively gives analytic step variation in t with larger time steps at apogee than at perigee, making errors at each point roughly comparable. In this paper, we develop techniques for assessing accuracy of s-integration in the presence of perturbations, and analyze the effectiveness of regularizing the transformed equations. A computational speed comparison is provided.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2002
Accession Number
ADA605040

Entities

People

  • Liam Healy
  • Matthew Berry

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Accuracy
  • Apogees
  • Artificial Satellites
  • Circular Orbits
  • Computational Science
  • Computations
  • Differential Equations
  • Eccentricity
  • Elliptical Orbits
  • Equations
  • Equations Of Motion
  • Errors
  • Military Research
  • Numerical Integration
  • Orbits
  • Perigees
  • Perturbations

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Space
  • Space - Orbital Debris