Abstract
The special perturbation method considered in this paper combines simplicity of computer implementation, speed and precision, and can propagate the orbit of any material particle. The paper describes the evolution of some orbital elements based in Euler parameters, which are constants in the unperturbed problem, but which evolve in the time scale imposed by the perturbation. The variation of parameters technique is used to develop expressions for the derivatives of seven elements for the general case, which includes any type of perturbation. These basic differential equations are slightly modified by introducing one additional equation for the time, reaching a total order of eight. The method was developed in the Grupo de Dinámica de Tethers (GDT) of the UPM, as a tool for dynamic simulations of tethers. However, it can be used in any other field and with any kind of orbit and perturbation. It is free of singularities related to small inclination and/or eccentricity. The use of Euler parameters makes it robust. The perturbation forces are handled in a very simple way: the method requires their components in the orbital frame or in an inertial frame. A comparison with other schemes is performed in the paper to show the good performance of the method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Awad M.E.-S. (1993) Oblateneess and drag effects on the motion of satellites in the set of Eulerian redundant parameters. Earth, Moon Planets 62(2): 161–177
Awad M.E.-S. (1995) Analytical solution to the perturbed J 2 motion of artificial satellites in terms of Euler parameters. Earth, Moon Planets 69(1): 1–12
Bond V.R. (1974) The uniform, regular differential equations of the KS transformed perturbed two-body problem. Celest. Mech. 10(3): 303–318
Bond V.R., Allman M.C. (1996) Modern Astrodynamics: Fundamentals and Perturbation Methods. University Press, Princeton, New Jersey
Bond, V.R., Fraietta, M.F.: Elimination of secular terms from the differential equations for the elements of the perturbed two-body problem. In: Proceedings of the Flight Mechanics and Estimation Theory Symposium, NASA (1991)
Bond, V.R., Horn, M.K.: The Burdet formulation of the perturbed two body problem with total energy as an element. JSC Internal 73-FM-86, NASA (1973)
Deprit A., Elipe A., Ferrer S. (1994) Linearization: Laplace vs. Stiefel. Celest. Mech. Dyn. Astron. 58(2): 151–201
Mohammed Adel.Sharaf, Awad M.E.-S., Najmuldeen S.A.-S.A. (1992) Motion of artificial satellites in the set of Eulerian redundant parameters (III). Earth, Moon Planets 56(2): 141–164
Palacios M., Calvo C. (1996) Ideal frames and regularization in numerical orbit computation. J. Astron. Sci. 44(1): 63–77
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C. The Art of Scientific Computing (2nd edn). Cambridge University Press, Cambridge, New York (1992)
Roy, A.E.: Orbital Motion. Adam Hilger (1988)
Stiefel E.L., Scheifele G. (1971) Linear and Regular Celestial Mechanics. Springer Verlag, Berlin, New York
Vallado, D.A.: Fundamentals of Astrodynamics and Applications. MacGraw-Hill (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Peláez, J., Hedo, J.M. & de Andrés, P.R. A special perturbation method in orbital dynamics. Celestial Mech Dyn Astr 97, 131–150 (2007). https://doi.org/10.1007/s10569-006-9056-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10569-006-9056-3