Orbit propagation in minkowskian geometry

Roa Vicens, Javier and Pelaez Alvarez, Jesus (2015). Orbit propagation in minkowskian geometry. In: "25th AAS/AIAA Space Flight Mechanics Meeting", 11-15 ene 2015, Williamsburg, Estados Unidos. ISBN 978-0-87703-623-4. pp. 3047-3066.


Title: Orbit propagation in minkowskian geometry
  • 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
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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A more adequate description of perturbed hyperbolic orbits is found in the geometry underlying Minkowski space-time. Hypercomplex numbers appear naturally when describing vectors, rotations, and metrics in this geometry. The solution to the unperturbed hyperbolic motion is well known in terms of hyperbolic functions and the hyperbolic anomaly. From this, a general solution is derived through the Variation of Parameters technique. Hyperbolic geometry leads to a more coherent formulation. The evolution of the eccentricity vector is described by means of its components on the Minkowski plane. The orbital plane is defined in the inertial reference using quaternions, treated as particular instances of hypercomplex numbers. The performance of the proposed formulation is evaluated for integrating flyby trajectories of NEAR, Cassini, and Rosetta spacecraft. Improvements in accuracy have been observed in these cases, with no penalties on the computational time.

Funding Projects

UnspecifiedESP 2013-41634-PUnspecifiedUnspecifiedDynamical analysis, advanced orbital propagation, and simulation of complex space systems

More information

Item ID: 40304
DC Identifier: http://oa.upm.es/40304/
OAI Identifier: oai:oa.upm.es:40304
Official URL: http://www.space-flight.org/docs/2015_winter/2015_winter.html
Deposited by: Memoria Investigacion
Deposited on: 10 Nov 2016 09:46
Last Modified: 10 Nov 2016 09:46
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