Application of Gröbner bases to problems of movement of a particle

✍ Scribed by N.I. Ioakimidis; E.G. Anastasselou

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 608 KB
• Volume: 27
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(94)90046-9

✦ Synopsis

The cfassicd method of Grijbner bases for multivariate polynomials in computer alge bra 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 se well. The popular computer algebra system Maple V and the related standard package were used for this purpose and several possibilities of using Grijbner 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 Grijbner 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.