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

Authors : Djavvat KHADJİEV, İdris ÖREN, Gayrat BESHİMOV

Pages : 334-342

Doi:10.36890/iejg.1091348

View : 123 | Download : 9

Publication Date : 2022-10-31

Article Type : Research Paper

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 $Oinsert ignore into journalissuearticles values(3,R);$ , the special orthogonal group $SOinsert ignore into journalissuearticles values(3,R);$, Euclidean group $MOinsert ignore into journalissuearticles values(3,R);$, the special Euclidean group $MSOinsert ignore into journalissuearticles values(3,R);$ and Galileo groups $Gal_{1}insert ignore into journalissuearticles values(3,R);$ , $Gal^{+}_{1}insert ignore into journalissuearticles values(3,R);$ are obtained.
Keywords : Galilean group, invariant, figure, Euclidean geometry

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