Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-14T14:17:31.716Z Has data issue: false hasContentIssue false
  • English
  • Français

New Intermediaries for the Main Problem in Satellite Theory

Published online by Cambridge University Press:  12 April 2016

José M. Ferrándiz  and
Luis Floría
José M. Ferrándiz
Affiliation:
Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, 47011 Valladolid, Spain
Luis Floría
Affiliation:
Departamento de Matemática Aplicada a la Ingeniería, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, 47011 Valladolid, Spain

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

After reviewing the original approach leading to the introduction of intermediaries in Satellite Theory, a general procedure to define intermediaries for the Main Problem in this Theory is proposed. This procedure is susceptible to an intuitive interpretation analogous to solving a simple puzzle. The application of this method to the Main Problem allows us not only to recover the well known classical intermediaries but also to obtain several completely new ones, all admitting simple solutions.

Type
Part V General Celestial Mechanics and Stellar Dynamics
Information
International Astronomical Union Colloquium , Volume 132: Instability, Chaos and Predictability in Celestial Mechanics and Stellar Dynamics , 1993 , pp. 341 - 352
Copyright
Copyright © Nova Science Publishers 1993

References

[1] Aksnes, K.: 1970, Astron. J. 75, 1066–1076.CrossRefGoogle Scholar
[2] Brouwer, D.: 1946, Astron. J. 51, 223–231.CrossRefGoogle Scholar
[3] Brouwer, D.: 1958, Astron. J. 63, 433–328.CrossRefGoogle Scholar
[4] Brouwer, D.: 1959, Astron. J. 64, 378–397.CrossRefGoogle Scholar
[5] Brouwer, D. and Clemence, G.M.: 1961, Methods of Celestial Mechanics, Academic Press, New York and London.Google Scholar
[6] Brown, E.W.: 1892, Amer. J. Math. 14, 141–160.CrossRefGoogle Scholar
[7] Brown, E.W.: 1893, Amer. J. Math. 15, 244–263.CrossRefGoogle Scholar
[8] Brown, E.W.: 1895, Amer. J.Math. 17, 318–358.CrossRefGoogle Scholar
[9] Cid, R. and Lahulla, J.F.: 1969, “Perturbaciones ed corto periodo en el movimiento de un satelite artificial, en function de las variables de Hill”, Rev. Acad.Ciencias Zaragoza Serie 2α , 24, 159–165.Google Scholar
[10] Cid, R. and Lahulla, J.F.: 1971, “Aplicacion declas transformaciones de Lie a la eliminacion de terminos de corto periodo”, Vrania, 274, 177–184.Google Scholar
[11] Cid, R. and Lahulla, J.F.: 1971, “Perturbaciones de segundo orden y corto periodo, para el movimiento de un satelite artificial, en las variables de Hill”, Rev.Acad. Ciencias Zaragoza, Serie 2α , 26, 333–343.Google Scholar
[12] Deprit, A.: 1969, Celest. Mech. 1, 12–30.CrossRefGoogle Scholar
[13] Deprit, A.: 1981, Celest. Mech. 24, 111–153.CrossRefGoogle Scholar
[14] Deprit, A. and Ferrer, S.: 1987, Celest. Mech. 40, 335–343.CrossRefGoogle Scholar
[15] Ferrandiz, J.M. and Floria, L.: 1989, “Generacion sistematica de intermediarios en la Teoria del Satelite”, Actas de las XIV Jornadas Hispano-Lusas de Matematicas, Vol. III, 1207–1211.Google Scholar
[16] Ferrandiz, J.M. and Floria, L.: 1989-1990, Towards a Systematic Definition of Intermediaries in the Theory of Artificial Satellites (Unpublished manuscript).Google Scholar
[17] Garfinkel, B.: 1958, Astron. J. 63, 88–96.CrossRefGoogle Scholar
[18] Garfinkel, B.: 1959, Astron. J. 64, 270–272.CrossRefGoogle Scholar
[19] Garfinkel, B.: 1959, Astron. J. 64, 353–367.CrossRefGoogle Scholar
[20] Garfinkel, E.: 1964, Astron. J. 69, 223–229.CrossRefGoogle Scholar
[21] Garfinkel, B. and Aksnes, K.: 1970, Astron. J. 75, 85–91.CrossRefGoogle Scholar
[22] Gylden, H.: 1882-1883, Acta Mathematica 1, 77–92.CrossRefGoogle Scholar
[23] Gylden, H.: 1885-1886, Acta Mathematica 7, 125–172.CrossRefGoogle Scholar
[24] Hagihara, Y.: 1971, Celestial Mechanics, Vol. II, Part I (Perturbation Theory), MIT Press.Google Scholar
[25] Hill, G.W.: 1878, Amer. J. Math. l. pp. 5–26, 129-147, 245-260.CrossRefGoogle Scholar
[26] Hill, G.W.: 1886, Acta Mathematica 8, 1–36.CrossRefGoogle Scholar
[27] Hori, G.-i.: 1966, Publ. Astron. Soc. Japan 18, 287–296.Google Scholar
[28] Roy, A.E.: 1988, Orbital Motion (Third Edition), Adam Hilger, Bristol and Philadelphia.Google Scholar
[29] Sterne, T.E.: 1957, Astron. J. 62, 96.CrossRefGoogle Scholar
[30] Sterne, T.E.: 1958, Astron. J. 63, 28–40.CrossRefGoogle Scholar