Generalized logarithmic spirals for low-thrust trajectory design

Roa Vicens, Javier and Pelaez Alvarez, Jesus (2016). Generalized logarithmic spirals for low-thrust trajectory design. In: "AAS/AIAA Astrodynamics Specialist Conference 2015", 9-13 Ago 2015, Vail, Colorado, Estados Unidos. ISBN 978-0-87703-629-6. pp. 2917-2936.


Title: Generalized logarithmic spirals for low-thrust trajectory design
  • Roa Vicens, Javier
  • Pelaez Alvarez, Jesus
Item Type: Presentation at Congress or Conference (Article)
Event Title: AAS/AIAA Astrodynamics Specialist Conference 2015
Event Dates: 9-13 Ago 2015
Event Location: Vail, Colorado, Estados Unidos
Title of Book: AAS/AIAA Astrodynamics Conference 2015. Advances in the Astronautical Sciences Series
Date: 2016
ISBN: 978-0-87703-629-6
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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Shape-based approaches are practical for finding sub-optimal solutions during the preliminary design of low-thrust trajectories. Logarithmic spirals are the simplest, but of little practical interest due to having a constant flight-path angle. We prove that the same tangential thrust profile that generates a logarithmic spiral yields an entire family of generalized spirals. The system admits two integrals of motion, which are equivalent to the energy and the angular momentum equations. Three different subfamilies of spiral trajectories are obtained depending on the sign of the constant of the generalized energy: elliptic, parabolic, and hyperbolic. Parabolic spirals are equivalent to logarithmic spirals. Elliptic spirals are bounded; never escape to infinity and the trajectory is symmetric. Two types of hyperbolic spirals have been found: the first has only one asymptote; the second has two asymptotes, the trajectory is symmetric and never falls to the origin. The solution is obtained when solving rigorously the equations of motion with no prior assumptions. Closed-form expressions for both the trajectory and the time of flight are provided.

Funding Projects

Government of SpainESP2013-41634-PUnspecifiedUnspecifiedDynamical analysis, advanced orbit propagation and simulation of complex space systems”

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Item ID: 40431
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Deposited by: Memoria Investigacion
Deposited on: 10 Nov 2016 09:05
Last Modified: 10 Nov 2016 09:24
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