Application of Gröbner bases to problems of movement of a particle (Q1324423)

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.