Abstract
A software package for Mechanized Algebraic Operations (MAO) is described. With MAO one is able to manipulate on the computer Poisson series in literal form. The system is operational; it has application in the fields of celestial mechanics, astrodynamics, and nonlinear mechanics. Besides describing the system, the present paper suggests various techniques to prepare problems such that they lend themselves for an automated treatment with MAO. Optimized implementation of the general subroutines is discussed.
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Danby, J. M. A., Deprit, A., and Rom, A. R. M.: 1965, ‘The Symbolic Manipulation of Poisson Series’, Boeing Scientific Research Laboratories, Mathematical Note No. 432.
Deprit, A. and Delie, A.: 1965, ‘Trojan Orbits I. D'Alembert Series at L4’, Boeing document D1-82-0393.
Deprit, A. and Rom, A. R. M.: 1967a, ‘Asymptotic Representation of the Cycle of Van der Pol's Equation for Small Damping Coefficients’,Z. angew. Math. Phys. 18, 736–747.
Deprit, A. and Rom, A. R. M.: 1967b, ‘Computerized Expansion in Elliptic Motion’,Bull. Astron. 3, Centre National de la Recherche Scientifique, Paris.
Deprit, A. and Rom, A. R. M.: 1968a, ‘Poincaré's Continuation by Computers’,AIAA J. 6, 1234–1239.
Deprit, A. and Rom, A. R. M.: 1968b, ‘Natural Orbits of the First Kind in the Restricted Problem’,Icarus 9, 336–356.
Deprit, A. and Rom, A. R. M.: 1968c, ‘Lindstedt's Series on a Computer’,Astron. J. 73, 210–213.
Deprit, A. and Rom, A. R. M.: 1969, ‘The Main Problem of Satellite Theory for Small Eccentricities’, Boeing Document D1-82-0888; submitted toCelestial Mechanics for publication.
Deprit, A., Henrard, J., and Rom, A. R. M.: 1967, ‘Trojan Orbits. II: Birkhoff's Normalization’,Icarus 6, No. 3.
Deprit, A., Henrard, J., Price, J. F., and Rom, A. R. M.: 1969, ‘Birkhoff's Normalization’, Boeing Document D1-82-0829; to appear inCelestial Mechanics.
IBM SYSTEM/360 FORTRAN IV Language: 1966, File No. S360-25, Form C28-6515-5, pp. 88–89.
Rom, A. R. M.: 1961, ‘Manipulation of Algebraic Expressions’,Communications of the ACM 4, 398.
Scowen, R. S.: 1965, Algorithm 271, ACM Comm.
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Rom, A. Mechanized Algebraic Operations (MAO). Celestial Mechanics 1, 301–319 (1970). https://doi.org/10.1007/BF01231135
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DOI: https://doi.org/10.1007/BF01231135