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Ioakimidis, N. I.; Anastasselou, E. G.

Application of Gröbner bases to problems of movement of a particle. (English) Zbl 0823.70001

Comput. Math. Appl. 27, No. 3, 51-57 (1994).
The classical method of Gröbner bases for multivariate polynomials in computer algebra and the related Buchberger’s algorithm and its modifications for the computation of such bases are applied to some elementary problems of kinematics as well as to the classical Kepler- Newton problem in celestial mechanics, where, beyond the variables in the polynomials, a differential operator appears as well. The popular computer algebra system Maple V and the related standard package were used for this purpose and several possibilities of using Gröbner bases for the proof and/or the derivation of formulae in mechanics are illustrated.

Cited in 1 Document

MSC:

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70F05 Two-body problems
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
68W30 Symbolic computation and algebraic computation

Keywords:

multivariate polynomials; Buchberger’s algorithm; Kepler-Newton problem; differential operator; computer algebra system Maple V

Software:

Maple
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Full Text: DOI

References:

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