×

ATESAT: A symbolic processor for artificial satellite theory. (English) Zbl 1017.70500

Summary: Analytical theories for the artificial satellite motion involve operations with the so called Poisson series. Even if only a second order theory is required, the amount of terms involved is so huge, that it is almost an impossible task to carry out by hand the theory. Thus, algebraic manipulators are essential in this field, and even more, since general purpose manipulators are not completely satisfactory, specific manipulators are necessary. Aware of this fact, we build ATESAT (Automatization of Theories and Ephemeris in the artificial Satellite problem), that provides the automatic generation of programs for computing the ephemeris of the satellite from the analytical theory chosen. ATESAT is built with PSPC, an algebraic manipulator from our own, especially designed for manipulating Poisson series.

MSC:

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70-04 Software, source code, etc. for problems pertaining to mechanics of particles and systems
70F15 Celestial mechanics
Full Text: DOI

References:

[1] A. Abad, J.F. San Juan, PSPC: A poisson series processor coded in C, in: S. Kurzyńska et al. (Eds.), Dynamics and Astrometry of Natural and Artificial Celestial Bodies, Poznan, Poland, 1993, pp. 383–389
[2] A. Abad, J.F. San Juan, ATESAT: Software tool for obtaining automatically ephemeris from analytical simplifications, in: A. Elipe, P. Pâquet (Eds.), Conseil de L’Europe. Cahiers du Centre Européen de Géodynamique et de Séismologie, Luxembourg, 10, 1995, pp. 93–98
[3] Abad, A.; Juan, J. F. San: Pspclink: A coorperation between general symbolic and Poisson series processors. Journal of symbolic computation 24, 113-122 (1997) · Zbl 0880.70003
[4] Alfriend, K. T.; Coffey, S. L.: Elimination of the perigee in satellite problem. Celestial mechanics 32, 163-172 (1984) · Zbl 0542.70033
[5] Coffey, S. L.; Alfriend, K. T.: An analytical orbit prediction program generator. J. guidance, control and dynamics 7, 575-581 (1984)
[6] N.N. Bogoliubov, Y.A. Mitropolski, Asymptotic Methods in The Theory of Non-Linear Oscillations, Gordon and Breach, New York, 1961
[7] Broucke, R.; Garthwaite, K.: A programming system for analytical series expansions on a computer. Celestial mechanics 1, 271-284 (1969)
[8] Brouwer, D.: Solution of the problem of artificial satellite theory without drag. The astronomical journal 64, 378-397 (1959)
[9] D. Brouwer, G.M. Clemence, Methods of Celestial Mechanics, Academic Press, New York, 1961 · Zbl 0132.23506
[10] Cid, R.; Lahulla, J. F.: Perturbaciones de segundo orden y corto perı\acute{}odo para el movimiento de un satélite artificial, en las variables de Hill. Rev. acad. Ciencias de Zaragoza 26, 333-343 (1971)
[11] Coffey, S. L.; Deprit, A.: Third order solution to the Main problem in satellite theory. J. guidance, control and dynamics 5, 366-371 (1982) · Zbl 0508.70010
[12] R.R. Dasenbrock, A FORTRAN-based program for computerized algebraic manipulation, Tech. rep. National Research Laboratory Report, 8611, 1982
[13] Deprit, A.: Canonical transformations depending on a small parameter. Celestial mechanics 1, 12-30 (1969) · Zbl 0172.26002
[14] Deprit, A.: The elimination of the parallax in satellite theory. Celestial mechanics 24, 111-153 (1981) · Zbl 0492.70024
[15] Deprit, A.: Delaunay normalisations. Celestial mechanics 26, 9-21 (1982) · Zbl 0499.70019
[16] A. Deprit, L’Algèbre symbolique en mécanique céleste, in: S. Ferraz-Mello et al (Eds.), Dynamics, Ephemerides and Astrometry of The Solar System, IAU Symposium No. 72, Kluwer, Dordrecht, 1996, pp. 267–282
[17] Deprit, A.; Henrard, J.; Rom, A.: Analytical lunar ephemeris: Delaunay’s theory. The astronomical journal 76, 269-272 (1971) · Zbl 0216.50304
[18] Deprit, A.; Rom, A.: The Main problem of artificial satellite theory for small and moderate eccentricities. Celestial mechanics 2, 166-206 (1970) · Zbl 0199.60101
[19] Deprit, A.; Ferrer, S.: Simplifications in the theory of artificial satellites. Journal of the astronautical sciences 37, 464-541 (1989)
[20] Deprit, A.; Miller, B.: Simplify or perish. Celestial mechanics 45, 189-200 (1989) · Zbl 0674.70004
[21] A. Deprit, J. Palacián, The Relegation Simplification (manuscript in preparation), 1997
[22] Henrard, J.: On a perturbation theory using Lie transforms. Celestial mechanics 3, 107-120 (1970) · Zbl 0223.70011
[23] Henrard, J.: A survey on Poisson series processors. Celestial mechanics 45, 245-253 (1989)
[24] Kozai, Y.: Second order solution of artificial satellite theory without drag. The astronomical journal 67, 446-461 (1962)
[25] K.R. Meyer, G.R. Hall, Introduction to Hamiltonian dynamical systems and the N-body problem, Applied Mathematical Sciences, vol. 90, Springer, New York, 1992 · Zbl 0743.70006
[26] Osácar, C.; Palacián, J.: Decomposition of functions for elliptic orbits. Celes. mech. & dynam. Astron. 60, 207-223 (1994) · Zbl 0822.70008
[27] J.F. Palacián, Teorı\acute{}a del satélite artificial: Armónicos teserales y su relegación mediante simplificaciones algebraicas, Ph.D. thesis, Universidad de Zaragoza, 1992
[28] Rom, A.: Mechanized algebraic operations (MAO). Celestial mechanics 1, 301-319 (1970) · Zbl 0193.15203
[29] J.F. San-Juan, Manipulación algebraica de series de poisson. Aplicación a la teorı\acute{}a del satélite artificial, Ph.D. thesis, Universidad de Zaragoza, 1996
[30] S. Wolfram, MathematicaTM, A System for Doing Mathematics by Computer, Addison-Wesley, Reading, MA, 1988 · Zbl 0671.65002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.