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APPLICATION OF THE FUNDAMENTAL EQUATION TO
CELESTIAL MECHANICS AND ASTRODYNAMICS
by
Darren David Garber
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ASTRONAUTICAL ENGINEERING)
May 2012
Copyright 2012 Darren David Garber
Object Description
| Title | Application of the fundamental equation to celestial mechanics and astrodynamics |
| Author | Garber, Darren David |
| Author email | darren.garber@nxtrac.com;darren.garber@nxtrac.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Astronautical Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2012-02-29 |
| Date submitted | 2012-03-29 |
| Date approved | 2012-03-30 |
| Restricted until | 2012-03-30 |
| Date published | 2012-03-30 |
| Advisor (committee chair) |
Gruntman, Michael Udwadia, Firdaus E. |
| Advisor (committee member) |
Erwin, Daniel A. Hintz, Gerald Effroimsky, Michael |
| Abstract | This paper proposes a new general approach for describing, generating and controlling the trajectory of an object by combining recent advances in analytical dynamics with the underlying theorems and concepts from differential geometry. By using the geometric construct of curvature to define an object’s motion and applying the fundamental equation of constrained dynamics, the resulting solutions are both explicit and exact for the minimum acceleration necessary to maintain the specified trajectory. The equations detailing the control force required to follow the selected trajectory can be expressed in closed form, regardless if the object is in Keplerian free-flight about a single central body or following a non-Keplerian trajectory in a highly disturbed environment. Examples are provided in both the inertial and non-inertial frames to demonstrate the utility of this combined approach for solving common problems in both celestial mechanics and astrodynamics. The practical aspects of exploiting curvature for maneuver and mission planning is also investigated resulting in the formulation of the Generalized Transfer Equation which extends the method of patched conics to include any curve. |
| Keyword | non-keplerian motion; astrodynamics; perturbations; maneuver planning; curvature; analytical dynamics; fundamental equation |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Contributing entity | University of Southern California |
| Rights | Garber, Darren David |
| Physical access | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@dots.usc.edu |
| Archival file | uscthesesreloadpub_Volume3/etd-GarberDarr-561.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@dots.usc.edu |
| Full text | APPLICATION OF THE FUNDAMENTAL EQUATION TO CELESTIAL MECHANICS AND ASTRODYNAMICS by Darren David Garber A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ASTRONAUTICAL ENGINEERING) May 2012 Copyright 2012 Darren David Garber |
