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2019 | OriginalPaper | Chapter

4. Two-Body Maneuvers with Unbounded Continuous Inputs

Author : Ashish Tewari

Published in: Optimal Space Flight Navigation

Publisher: Springer International Publishing

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Abstract

A majority of spacecraft navigation problems involve transfers between two given positions and velocities. When continuous inputs are applied for the orbital transfer of a spacecraft around a central body, the perturbed two-body model can be used as a plant to derive the optimal trajectory and control history.

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previous chapter Orbital Mechanics and Impulsive Transfer
next chapter Optimal Maneuvers with Bounded Inputs
Footnotes
1
An osculating orbit is defined to be the tangential trajectory that will be followed if the perturbing acceleration were suddenly to be removed. If the perturbation is large and were suddenly to be removed, there would be an almost impulsive change in the acceleration at the instant of removal, which translates into a step change of velocity. Therefore, in that case the resulting orbit would not be tangential to the original (perturbed) orbit. In fact, there will be a “bump” in the trajectory. Hence the concept of osculating orbit is valid only if the applied perturbation is always small, so that at any instant, an abrupt vanishing of the acceleration would not cause an abrupt change in the velocity, thereby approximating the resulting orbit as being tangential (or osculating) to the original (perturbed) orbit.
 
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Edelbaum, T.N.: Optimal space trajectories. Analytical Mechanics Associates Report, No. 69-4, Jericho, New York (1969)
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Kechichian, J.A.: The algorithm of the two-impulse time-fixed noncoplanar rendezvous with drag and oblateness effects. In: Proceedings of AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 97-645, Sun Valley (1997)
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Tewari, A.: Modern Control Design with MATLAB and Simulink. Wiley, Chichester (2002)
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Tewari, A.: Advanced Control of Aircraft, Spacecraft, and Rockets. Wiley, Chichester (2011)CrossRef
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Yamanaka, K., Ankersen, F.: New state transition matrix for relative motion on an arbitrary elliptical orbit. J. Guid. Control. Dyn. 25, 60–66 (2002)CrossRef
Metadata
Title
Two-Body Maneuvers with Unbounded Continuous Inputs
Author
Ashish Tewari
Copyright Year
2019
Book
Optimal Space Flight Navigation

Print ISBN: 978-3-030-03788-8

Electronic ISBN: 978-3-030-03789-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-03789-5_4