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L'algèbre symbolique en mécanique céleste

Published online by Cambridge University Press:  25 May 2016

André Deprit*
Affiliation:
National Institute of Standards and Technology, Gaithersburg, MD 20899–0001, U.S.A.

Extract

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Que dire de l'algèbre symbolique en mécanique céleste si ce n'est que les astronomes furent les premiers sur le chantier. Rien là qui doive surprendre.

Type
Part VII - The Calculus of Perturbations
Copyright
Copyright © Kluwer 1996 

References

Abad Medina, A., Elipe Sánchez, A. and Vallejo Carrión, M.: 1994, “Automated Fourier series expansions for elliptic functions”, Mechanics Research Communic. 21, 361366.CrossRefGoogle Scholar
Abad Medina, A.:1995, “Integrales y funciones elípticas”, Grupo de Mecánica espacial, Universidad de Zaragoza (Spain), in preparation.Google Scholar
Abelson, H. and Sussman, G. J.: 1986, Structure and interpretation of computer programs, The MIT Press, Boston, MA.Google Scholar
Barton, D. and Fitch, J. P.: 1972, “Applications of algebraic manipulative programs in physics”, Reports on Progress in Physics, 35, 235314.Google Scholar
Bretagnon, P. and Francou, G.: 1988, “Planetary Theories in rectangular and spherical variables. VSOP87 solutions”, Astronomy and Astrophysics 202, 309315.Google Scholar
Brouwer, D.: 1958, “Celestial mechanics conference”, Astronomical Journal, 63, 401463.Google Scholar
Brumberg, V.: 1995, Analytical Techniques of Celestial Mechanics, Springer-Verlag, Berlin.CrossRefGoogle Scholar
Byrd, P. F. and Friedman, M. D.: 1954, Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, Berlin/Göttingen/Heidelberg.Google Scholar
Chapront-Touzé, M. and Chapront, J.: 1988, “ELP 2000–85: a semi-analytical lunar ephemeris adequate for historical times”, Astronomy and Astrophysics 190, 342352.Google Scholar
Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B. and Watt, S. M.: 1991, Maple V Language Reference Manual, Springer-Verlag, Berlin.Google Scholar
Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B. and Watt, S. M.: 1991, Maple V Library Reference Manual, Springer-Verlag, Berlin.Google Scholar
Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B. and Watt, S. M.: 1992, First Leaves: A Tutorial Introduction to Maple V, Springer-Verlag.Google Scholar
Coffey, S. L., Deprit, A. and Miller, B.: 1986, “The critical inclination in artificial satellite theory”, Celestial Mechanics 39, pp. 365406.Google Scholar
Deprit, A. and López Moratalla, T., “Estabilidad de satélites geoestacionarios”, Revista matemática de la Universidad Complutense de Madrid, accepted for publication.Google Scholar
de Vogelaere, R.: 1958, “On the structure of symmetric periodic solutions of conservative systems, with applications ”, in Contributions to the theory of nonlinear oscillations Vol. IV, ed. Lefschetz, S., Annals of Mathematical Studies 41, 5384.Google Scholar
Duncombe, R. L.: 1988, “Early applications of computer technology to dynamical astronomy”, Celestial Mechanics 45, pp. 110.Google Scholar
Eckert, W.: 1957, “Computing in Astronomy”, in The Computing Laboratory, ed. Hammer, P. R., pp.4350, The University of Wisconsin Press, Madison, WI.Google Scholar
Fateman, R. H.: 1991, “A review of Mathematica”, J. of Symbolic Comput. 13., 353394.Google Scholar
Fateman, R. H. and Berman, B.: 1994, “Optical character recognition for typeset mathematics”, in Proceedings, ISSAC, Oxford, UK, July 1994, pp. 348353.Google Scholar
Foster, K. R. and Bau, H. H.: 1989, “Symbolic Manipulation programs for Personal Computers”, Science 243, 679684.Google Scholar
Geddes, K. O., Czapor, S. R. and Labahn, G.: 1992, Algorithms for Computer Algebra, Kluwer Academic Publishers, Boston/Dordrecht/London.CrossRefGoogle Scholar
Gradshteyn, I. S. and Ryzhik, I. M.: 1980, Table of Integrals, Series and Products, Academic Press, New York/London/Toronto/Sydney/San Francisco.Google Scholar
Graves, W. M. H.: 1953, “Leslie John Comrie”, Monthly Notices of the Royal Astronomical Society 113, 294304.Google Scholar
Gutzwiller, M. and Schmidt, D.: 1986, “The Motion of the Moon as computed by the Method of Hill, Brown, and Eckert”, Astronomical Papers 23, Part I.Google Scholar
Henrard, J.: 1988, “A survey of Poisson series”, Celestial Mechanics 45, 245254.Google Scholar
Hillis, W. D.: 1985, The Connection Machine, MIT Press, Cambridge MA.Google Scholar
Jenks, R. D. and Sutor, R. S.: 1992, AXIOM: the scientific computation system, Springer-Verlag, Berlin.Google Scholar
Knuth, D.: 1969, The Art of Computer Programming, chapter 4, Addison-Wesley Publishing Company, Menlo Park, CA.Google Scholar
Kovalevsky, J.: 1958, “The problems of the eight satellite of Jupiter”, Astronomical Journal 63, 452456.Google Scholar
Kovalevsky, J.: 1959, “Méthode numérique de calcul des perturbations générales. Application au VIIIe satellite de Jupiter”, Thèses présentées à la Faculté des Sciences de l'Université de Paris Série A n° 3369, Gauthier-Villars, Paris.Google Scholar
Macsyma, : 1995, Mathematics and system reference manual. Version 15, Macsyma Inc., Arlington, MA.Google Scholar
Moses, J.: 1971, “Algebraic Simplifications: A Guide to the Perplexed”, Communications of the ACM 14, 527537.Google Scholar
Poggendorff, J. C.: 1863, Biographisch-Literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften, Verlag von Johann Ambrosius Barth, Leipzig.Google Scholar
Simon, B.: 1990, “Four computer mathematical environments”, Notices of the American Mathematical Society 37, 861868.Google Scholar
Steele, G. L. Jr., Fahlman, S. E., Gabriel, R. P., Moon, D. A. and Weinreb, D. L.: 1992, Common Lisp: the language, Digital Press, Burlington, MA.Google Scholar
Vallejo Carrión, M.: 1995, “Series de Fourier de funciones elípticas. Aplicación a la precesión terrestre”, Doctoral dissertation, Universidad de Zaragoza, reprinted in Boletín 2/95, Real Instituto y Observatorio de la Armada, San Fernando (Cádiz).Google Scholar
Wolfram, S.: 1991, Mathematica. A system for doing mathematics by computer, Addison-Wesley Publishing Co., Redwood City, CA.Google Scholar