Complete systems of Galileo invariants of a motion of parametric figure in the three dimensional Euclidean space

Abstract

Let E_{3} be the 3-dimensional Euclidean space and S be a set such that it has at least two elements. A definition of an S-parametric figure in E_{3} and a definition of a motion of an S-parametric figure in E_{3} are given. Complete systems of G-invariants of a parametric figure in E_{3} for fundamental groups of transformations of E_{3} have obtained. A complete system of G-invariants of a motion of a parametric figure in E_{3} for the Galileo groups Gal_{1}(3,R), Gal^{+}_{1}(3,R) of transformations of E_{3} have obtained.