Introducing a degree of freedom in the family of generalized logarithmic spirals

Roa, Javier and Pelaez Alvarez, Jesus (2016). Introducing a degree of freedom in the family of generalized logarithmic spirals. "Advances in the Astronautical Sciences", v. 158 ; pp. 299-318. ISSN 1081-6003.

Description

Title: Introducing a degree of freedom in the family of generalized logarithmic spirals
Author/s:
  • Roa, Javier
  • Pelaez Alvarez, Jesus
Item Type: Article
Título de Revista/Publicación: Advances in the Astronautical Sciences
Date: 2016
Volume: 158
Subjects:
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Física Aplicada a las Ingenierías Aeronáutica y Naval
UPM's Research Group: Dinámica Espacial SDG-UPM
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The versatility of the family of generalized logarithmic spirals is improved by introducing a degree of freedom in the solution. The low-thrust acceleration profile now includes a control term that affects both the magnitude and the direction of the thrust. Exact and fully analytic solutions to the trajectory, the velocity, the time of flight, etc. are made available. Two integrals of motion are preserved. The first one is a generalization of the equation of the energy and depends on the values of the control parameter. The second one relates to the equation of the angular momentum. The problem of finding spiral transfers between two arbitrary state vectors reduces to solving one algebraic equation with one unknown. The degree of freedom allows fixing the time of flight of the transfer. If the time of flight is fixed, then there are two equations with two unknowns. No other iterative procedures are required. Coast arcs can be introduced in the solution naturally. An explicit expression for the maximum acceleration reached along the transfer is provided. Thanks to the symmetry properties of the solution a simple algorithm for generating periodic orbits is presented. An arbitrary number of intermediate nodes can be introduced to improve the flexibility of the solution when facing optimization problems. An example of a low-thrust gravityassist Earth-Mars-Ceres trajectory shows that the solution is comparable to that obtained with other preliminary design techniques.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainESP2013-41634-PUnspecifiedUnspecifiedAnálisis dinámico, propagación orbital avanzada y simulación de sistemas espaciales complejos

More information

Item ID: 52046
DC Identifier: http://oa.upm.es/52046/
OAI Identifier: oai:oa.upm.es:52046
Deposited by: Memoria Investigacion
Deposited on: 11 Oct 2018 11:02
Last Modified: 11 Oct 2018 11:02
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