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

Author

Michael P. Ward

Date of Award

12-1990

Document Type

Thesis

Degree Name

Master of Science

Department

Department of Aeronautics and Astronautics

First Advisor

Rodney Bain, PhD

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.

AFIT Designator

AFIT-GA-ENY-90D-14

DTIC Accession Number

ADA230545

Comments

The author's Vita page is omitted.

Recommended Citation

Ward, Michael P., "A Numerical Investigation of the Series Reversion/Inversion and Series Reversion of Lambert's Time Function" (1990). Theses and Dissertations. 7907.
https://scholar.afit.edu/etd/7907