Regularized formulations in relative motion

Roa Vicens, Javier and Pelaez Alvarez, Jesus (2015). Regularized formulations in relative motion. In: "25th AAS/AIAA Space Flight Mechanics Meeting", 11-15 ene 2015, Williamsburg, Estados Unidos. ISBN 978-0-87703-623-4. pp. 2015-2034.

Description

Title: Regularized formulations in relative motion
Author/s:
  • Roa Vicens, Javier
  • Pelaez Alvarez, Jesus
Item Type: Presentation at Congress or Conference (Article)
Event Title: 25th AAS/AIAA Space Flight Mechanics Meeting
Event Dates: 11-15 ene 2015
Event Location: Williamsburg, Estados Unidos
Title of Book: AAS/AIAA Space Flight Mechanics Meeting 2015. Advances in the Astronautical Sciences Series
Date: 2015
ISBN: 978-0-87703-623-4
ISSN: 1081-6003
Volume: 155
Subjects:
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Física Aplicada a las Ingenierías Aeronáutica y Naval
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

Variational methods based on orbital elements depend strongly on the eccentricity of the reference orbit. The resulting Jacobian matrix typically becomes singular when the reference orbit is parabolic or hyperbolic. This singularity can be avoided if the problem is formulated using sets of variables that do not depend on the eccentricity of the reference orbit. The solution to the linear equations of relative motion is derived in this paper from the Sperling-Burdet regularization and the Kustaanheimo-Stiefel transformation. A unified description for circular, elliptic, parabolic, and hyperbolic reference orbits is provided by means of the Stumpff functions. The independent variable is the fictitious time introduced by the Sundman transformation. An asynchronous solution is derived and corrected a posteriori. The first order correction recovers the synchronism, while a second order correction introduces nonlinear effects and improves the accuracy of the algorithm.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainESP2013-41634-PUnspecifiedJesús Peláez ÁlvarezDynamical analysis, advanced orbital propagation, and simulation of complex space systems

More information

Item ID: 40303
DC Identifier: http://oa.upm.es/40303/
OAI Identifier: oai:oa.upm.es:40303
Official URL: http://space-flight.org/docs/2015_winter/2015_winter.htm
Deposited by: Memoria Investigacion
Deposited on: 10 Nov 2016 09:53
Last Modified: 06 Mar 2019 08:14
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