Spiral Lambert's problem with generalized logarithmic spirals

Roa Vicens, Javier and Pelaez Alvarez, Jesus (2016). Spiral Lambert's problem with generalized logarithmic spirals. In: "26th AAS/AIAA Space Flight Mechanics Meeting", 14-18 feb 2016, Napa, California. ISBN 978-0-87703-633-3. pp. 1-20.


Title: Spiral Lambert's problem with generalized logarithmic spirals
  • Roa Vicens, Javier
  • Pelaez Alvarez, Jesus
Item Type: Presentation at Congress or Conference (Article)
Event Title: 26th AAS/AIAA Space Flight Mechanics Meeting
Event Dates: 14-18 feb 2016
Event Location: Napa, California
Title of Book: Spaceflight Mechanics Meeting 2016
Date: 2016
ISBN: 978-0-87703-633-3
Volume: 158 IV
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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Lambert?s problem subject to a continuous acceleration is solved using the family of generalized logarithmic spirals. Thanks to the existence of two first integrals related to the energy and angular momentum surprising analogies with the Keplerian case are found. A minimum-energy spiral transfer exists. Increasing the value of the constant of the generalized energy yields pairs of conjugate spiral trajectories. The properties of such spirals are strongly connected with the properties of conjugate Keplerian orbits. When the generalized constant of the energy reaches a critical value the two solutions degenerate into a pair of parabolic spirals, one of which connects the two vectors through infinity. From that point the spiral transfers become hyperbolic. Generalized logarithmic spirals admit closed-form solutions to all the required magnitudes including the time of flight, providing a deep insight into the dynamics of the problem. In addition, the maximum acceleration along the transfer is found analytically so the solutions that violate the design constraints on the maximum thrust acceleration can be rejected without any further computations. When the time of flight is fixed there is still a degree of freedom in the solution, related to a control parameter. Resonant transfers appear naturally thanks to the symmetry properties of the generalized logarithmic spirals. The problem of designing a low-thrust transfer between two bodies can be reduced to solving the corresponding spiral Lambert?s problem. In order to show the versatility of the method it is applied to the design of an asteroid tour and to explore launch opportunities to Mars.

Funding Projects

Government of SpainESP2013-41634-PUnspecifiedJesus Peláez AlvarezAnálisis dinámico, propagación orbital avanzada y simulación de sistemas espaciales complejos

More information

Item ID: 52191
DC Identifier: https://oa.upm.es/52191/
OAI Identifier: oai:oa.upm.es:52191
Official URL: https://www.space-flight.org/docs/2016_winter/2016_winter.html
Deposited by: Memoria Investigacion
Deposited on: 15 Mar 2019 09:09
Last Modified: 15 Mar 2019 09:09
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