A Numerical Investigation of the Series Reversion/Inversion and Series Reversion of Lambert's Time Function

Abstract

An expression for the semi-major axis as a function of time may be determined by performing a series reversion and inversion of Lambert's Time Function. Since the resulting series contains a singularity, it is desirable to perform only a reversion on the original series to obtain an expression for the inverse of the semi-major axis. Using a Lagrange expansion to obtain the coefficients for this series is very computer intensive. Therefore, alternative methods are presented. Also, each series was expanded into a continued fraction which provided greater accuracy than the series using the same number of coefficients. The accuracy was found to be dependent upon the number of series coefficients used, the transfer time, and the transfer angle.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1990
Accession Number
ADA230545

Entities

People

  • Michael P Ward

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Abstracts
  • Accuracy
  • Air Force
  • Air Force Facilities
  • Availability
  • Celestial Mechanics
  • Coefficients
  • Computers
  • Energy Transfer
  • Engineering
  • Equations
  • Mechanics
  • Orbital Mechanics
  • Orbits
  • Polynomials
  • Time Intervals
  • Trajectories

Readers

  • Chemistry (specifically Chemical Fluorescence)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Space Exploration and Orbital Mechanics.