Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space

Year 2022, Volume: 15 Issue: 2, 334 - 342, 31.10.2022

Djavvat Khadjiev , İdris Ören , Gayrat Beshimov

https://doi.org/10.36890/iejg.1091348

Abstract

Let $E^{3}$ be the 3-dimensional Euclidean space and $S$ be a set with at least two elements. The notions of an $S$-parametric figure and the motion of an $S$-parametric figure in $E^{3}$ are defined. Complete systems of invariants of an $S$-parametric figure in $E^{3}$ for the orthogonal group $O(3,R)$ , the special orthogonal group $SO(3,R)$, Euclidean group $MO(3,R)$, the special Euclidean group $MSO(3,R)$ and Galileo groups $Gal_{1}(3,R)$ , $Gal^{+}_{1}(3,R)$ are obtained.

Keywords

Galilean group, invariant, figure, Euclidean geometry

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