2024-03-29T09:45:20Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1569052024-03-01T08:22:52Zcom_10234_7037com_10234_9col_10234_8635
00925njm 22002777a 4500
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López Ortí, José Antonio
author
Marco Castillo, Francisco José
author
Martínez Usó, María José
author
2016
This paper is aimed to address the study of techniques focused on the use of a family of anomalies based on a family of geometric transformations that includes the true anomaly f, the eccentric anomaly g and the secondary anomaly f′ defined as the polar angle with respect to the secondary focus of the ellipse.
This family is constructed using a natural generalization of the eccentric anomaly. The use of this family allows closed equations for the classical quantities of the two body problem that extends the classic, which are referred to eccentric, true and secondary anomalies.
In this paper we obtain the exact analytical development of the basic quantities of the two body problem in order to be used in the analytical theories of the planetary motion. In addition, this paper includes the study of the minimization of the errors in the numerical integration by an appropriate choice of parameters in our selected family of anomalies for each value of the eccentricity.
LÓPEZ ORTÍ, José A.; MARCO CASTILLO, Francisco José; MARTÍNEZ USÓ, María José. Geometrical definition of a continuous family of time transformations generalizing and including the classic anomalies of the elliptic two-body problem. Journal of Computational and Applied Mathematics, 2016.
0377-0427
http://hdl.handle.net/10234/156905
http://dx.doi.org/10.1016/j.cam.2016.02.041
celestial mechanics
orbital motion
ordinary differential equations
computational algebra
Geometrical definition of a continuous family of time transformations generalizing and including the classic anomalies of the elliptic two-body problem