A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion
The orbital motion around a central body is an interesting problem that involves the theory of artificial satellites and the planetary theories in the solar system. Nevertheless some difficult situations appear while studying this apparently simple problem, depending on each particular case. The rea...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/691926 |
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| author | José Antonio López Ortí Francisco José Marco Castillo María José Martínez Usó |
| author_facet | José Antonio López Ortí Francisco José Marco Castillo María José Martínez Usó |
| author_sort | José Antonio López Ortí |
| collection | DOAJ |
| description | The orbital motion around a central body is an interesting problem
that involves the theory of artificial satellites and the planetary theories
in the solar system. Nevertheless some difficult situations appear while
studying this apparently simple problem, depending on each particular
case. The real problem consists of searching the perturbed solution from
a basic two-body motion problem. In addition, the perturbed problem
must be solved using a numerical method and its efficiency depends on
the selected coordinate system and the corresponding time. In fact, local
and global errors are not necessarily homogeneously distributed over the
orbit. In other words, there is a strong relationship between the spatial
distribution of the selected points and the temporal independent variable.
This is particularly dramatic in specially difficult cases.
This issue leads us to consider different anomalies as temporal variables, searching for both precision and efficiency. Therefore, we are interested in the study of techniques to integrate the orbital motion equations
using different anomalies as temporal variables which are functions of one
or more parameters. The final aim of this paper is the minimization of the integration errors using an appropriate choice of the parameter depending on the eccentricity
value in the family of the generalized Sundman anomalies. |
| format | Article |
| id | doaj-art-d7160dd043c3407ba16d01c56f55bbc5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d7160dd043c3407ba16d01c56f55bbc52025-02-03T01:11:27ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/691926691926A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital MotionJosé Antonio López Ortí0Francisco José Marco Castillo1María José Martínez Usó2Departamento de Matemáticas, Instituto de Matemáticas y Aplicaciones de Castellón, Universidad Jaume I de Castellón, 12071 Castellón, SpainDepartamento de Matemáticas, Instituto de Matemáticas y Aplicaciones de Castellón, Universidad Jaume I de Castellón, 12071 Castellón, SpainDepartamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46022 Valencia, SpainThe orbital motion around a central body is an interesting problem that involves the theory of artificial satellites and the planetary theories in the solar system. Nevertheless some difficult situations appear while studying this apparently simple problem, depending on each particular case. The real problem consists of searching the perturbed solution from a basic two-body motion problem. In addition, the perturbed problem must be solved using a numerical method and its efficiency depends on the selected coordinate system and the corresponding time. In fact, local and global errors are not necessarily homogeneously distributed over the orbit. In other words, there is a strong relationship between the spatial distribution of the selected points and the temporal independent variable. This is particularly dramatic in specially difficult cases. This issue leads us to consider different anomalies as temporal variables, searching for both precision and efficiency. Therefore, we are interested in the study of techniques to integrate the orbital motion equations using different anomalies as temporal variables which are functions of one or more parameters. The final aim of this paper is the minimization of the integration errors using an appropriate choice of the parameter depending on the eccentricity value in the family of the generalized Sundman anomalies.http://dx.doi.org/10.1155/2014/691926 |
| spellingShingle | José Antonio López Ortí Francisco José Marco Castillo María José Martínez Usó A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion Abstract and Applied Analysis |
| title | A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion |
| title_full | A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion |
| title_fullStr | A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion |
| title_full_unstemmed | A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion |
| title_short | A Note on the Use of Generalized Sundman Anomalies in the Numerical Integration of the Elliptical Orbital Motion |
| title_sort | note on the use of generalized sundman anomalies in the numerical integration of the elliptical orbital motion |
| url | http://dx.doi.org/10.1155/2014/691926 |
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