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MathATESAT: A Symbolic-Numeric Environment in Astrodynamics and Celestial Mechanics

  • Juan Félix San-Juan
  • Luis María López
  • Rosario López
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6783)

Abstract

The increase in the facilities of the general computer algebra system, in particular Mathematica, and hardware evolution have supplied us with the possibility of developing a new environment called MathATESAT. Our new system collects all the tools necessary to carry out high accuracy analytical theories in order to analyze the quantitative and qualitative behaviour of a dynamic system. Real applications for the calculation of several expansions of Disturbing Functions, classical expansions of the Kepler problem and some details involved in the qualitative analysis of dynamic systems, are used to illustrate the capability of MathATESAT.

Keywords

General computer algebra Mathematica Poisson Series Astrodynamics 

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References

  1. 1.
    Herget, P., Musen, P.: The calculation of literal expansions. Astron. J. 71, 11–20 (1959)CrossRefGoogle Scholar
  2. 2.
    San-Juan, J.F., López, R.: Astrody Web Tools: Astrodynamics Web Tools. In: Lanchares, V., Elipe, A. (eds.) Monografías de la Real Academia de Ciencias de Zaragoza, vol. 32, pp. 105–114 (2009)Google Scholar
  3. 3.
    San-Juan, J.F., López, R.: NonDy\(^{\mathcal{W}eb}_{\mathcal{T}ools}\) an e-Science and e-Learning project. In: León, M., Martín, D., Ros, R. (eds.) Mathematics and Astronomy: A Joint Long Journey. AIP Conference Proceedings, vol. 1283, pp. 207–214 (2009)Google Scholar
  4. 4.
    San-Juan, J.F.: ATESAT: Automatization of theories and ephemeris in the artificial satellite problem. Tech. rep. CT/TI/MS/MN/94-250, CNES France (1994)Google Scholar
  5. 5.
    San-Juan, J.F.: Manipulación algebraica de series de Poisson. Aplicación a la teoría del satélite artificial. Ph.D. dissertation, Universidad de Zaragoza, Spain (1996)Google Scholar
  6. 6.
    San-Juan, J.F.: ATESAT: review and improvements. Study of a family of analytical models of the artificial satellite generated by ATESAT and their numerical validation versus PSIMU and MSLIB. Technical Report No. DGA/T/TI/MS/MN/97-258, CNES France (1998)Google Scholar
  7. 7.
    Wolfram Research, Inc.: Mathematica Edition: Version 6.0. Wolfram Research, Inc. Champaign, Illinois (2007)Google Scholar
  8. 8.
    Wolfram Research, Inc.: Mathematica Edition: Version 7.0. Wolfram Research, Inc. Champaign, Illinois (2008)Google Scholar
  9. 9.
    Abad, A., San-Juan, J.F.: Algebraic and Symbolic Manipulation of Poisson Series. J. Symb. Comp. 32(5), 565–572 (2001)CrossRefzbMATHGoogle Scholar
  10. 10.
    Deprit, A.: Canonical transformations depending on a small parameter. Celes. Mech. & Dynam. Astron. 1(1), 12–30 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Henrard, J.: On a perturbation theory using Lie Transform. Celes. Mech. & Dynam. Astron. 3(1), 107–120 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kamel, A.A.: Perturbation methods in the theory of nonlinear oscillations. Celes. Mech. & Dynam. Astron. 3(1), 90–106 (1970)CrossRefzbMATHGoogle Scholar
  13. 13.
    Krylov, N., Bogoliubov, N.N.: Introduction to Nonlinear Mechanics. Princeton University Press, Princeton (1947)zbMATHGoogle Scholar
  14. 14.
    Bogoliubov, N.N., Mitropolsky, Y.A.: Asymptotic Method in the Theory of Nonlinear Oscillations. Gordon and Breach, New York (1961)Google Scholar
  15. 15.
    Kaula, W.: Theory of Satellite Geodesy. Blaisdale Press, Waltham (1966)zbMATHGoogle Scholar
  16. 16.
    Hansen, P.A.: Entwickelung des Products einer Potenz des Radius Vector mit dem Sinus oder Cosinus eines Vielfachen der wahren Anomalie in Reihen. Abhandl. d. K. S. Ges. d. Wissensch 2, 183–281 (1853)Google Scholar
  17. 17.
    Cayley, A.: Tables of the Developments of Functions in the Theory of Elliptic Motion. Mem. Roy. Astron. Soc. 2, 191–306 (1861)Google Scholar
  18. 18.
    Newcomb, S.: Development of the perturbative function in cosines of multiples of the mean anomalies and of angles between the perihelia and common node and in powers of the eccentricities and mutual inclinations. Astr. Pap. 5, 1–48 (1895)Google Scholar
  19. 19.
    Deprit, A., Deprit, E.: Processing Poisson series in parallel. J. Symb. Comp. 10(2), 179–201 (1990)CrossRefzbMATHGoogle Scholar
  20. 20.
    Ferrer, S., San-Juan, J.F., Abad, A.: A note on lower bounds for relative equilibria in the main problem of artificial satellite theory. Celes. Mech. & Dynam. Astron. 99(1), 69–83 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Juan Félix San-Juan
    • 1
  • Luis María López
    • 2
  • Rosario López
    • 1
  1. 1.Departamento de Matemáticas y ComputaciónUniversidad de La RiojaLogroñoSpain
  2. 2.Departamento de Ingeniería MecánicaUniversidad de La RiojaLogroñoSpain

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