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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Notes
- 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.
References
Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. AIAA Education Series, Reston (1999)
Chobotov, V.A. (ed.): Orbital Mechanics, Chap. 14. AIAA Education Series, Reston (2002)
Clohessy, W.H., Wiltshire, R.S.: Terminal guidance system for satellite rendezvous. J. Aerospace Sci. 27, 653–658 (1960)
Edelbaum, T.N.: Optimal space trajectories. Analytical Mechanics Associates Report, No. 69-4, Jericho, New York (1969)
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)
Tewari, A.: Modern Control Design with MATLAB and Simulink. Wiley, Chichester (2002)
Tewari, A.: Advanced Control of Aircraft, Spacecraft, and Rockets. Wiley, Chichester (2011)
Yamanaka, K., Ankersen, F.: New state transition matrix for relative motion on an arbitrary elliptical orbit. J. Guid. Control. Dyn. 25, 60–66 (2002)
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Tewari, A. (2019). Two-Body Maneuvers with Unbounded Continuous Inputs. In: Optimal Space Flight Navigation. Control Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-03789-5_4
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DOI: https://doi.org/10.1007/978-3-030-03789-5_4
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