Application of Gröbner bases to problems of movement of a particle
Loading...
Date
1994-02
Authors
Ioakimidis, Nikolaos
Anastasselou, Eleni
Journal Title
Journal ISSN
Volume Title
Publisher
Pergamon Press
Abstract
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, the differential operator D 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. The present results generalize well-known results for the proof/derivation of geometric theorems by using classical Gröbner bases and related techniques and they illustrate the power of commercial computer algebra systems in the aforementioned tasks in kinematics. Modifications and generalizations of the present approach are also possible.