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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

References

  • [1] Aripov R. and Khadjiev D.:The complete system of global differential and integral invariants of a curve in Euclidean geometry, Izvestiya Vuzov, Ser. Mathematics, 542, 1-14 (2007).(Russian). (English translation) Aripov R. and Khadzhiev D., Russian Mathematics (Iz VUZ), 2007, Vol. 51, No. 7, pp.1-14.
  • [2] BergerM.:Geometry I, Springer-Verlag,Berlin,Heidelberg,1987.
  • [3] ElleryB.G.:Foundations of Euclidean and Non-Euclidean Geometry,HoltRinehartand WinstonINC,NewYork,1968.
  • [4] Marvin,Y.G.:EuclideanandNon-EuclideanGeometries,W.H.FreemanandCompany,NewYork,1993.
  • [5] Ho ̋ferR.:m-pointinvariantsofrealgeometries,BeitrageAlgebraGeom,40,261-266(1999).
  • [6]O ̋ren I.,KhadjievD.and Peksen O.:Identificationsofpathsandcurvesundertheplanesimilaritytransformationsandtheirapplicationsto mechanics, Journal of Geometry and Physics, 151, (2020).
  • [7]KhadjievD.:CompletesystemsofdifferentialinvariantsofvectorfieldsinaEuclideanspace,TurkishJournalofMathematics,34,543-559(2010).
  • [8] KhadjievD.,O ̋renI.andPeks ̧enO ̋.:Globalinvariantsofpathsandcurvesforthegroupofalllinearsimilaritiesinthetwo-dimensionalEuclidean space, International Journal of Geometric Methods in Modern Physics, 15, No. 6, (2018).
  • [9] Khadjiev D.:Ayupov Sh. and Beshimov G.:Complete systems of invariants of m-tuples for fundamental groups of the two-dimensional Euclidean space, Uzbek Mathematical Journal, 1,71-98 (2020,).
  • [10] KhadjievD.,BekbaevU.,AripovR.:Onequivalenceofvector valuedmaps,arXiv:2005.08707v1[mathGM]13May2020.
  • [11] PatricJ.R.:EuclideanandNon-EclideanGeometry,AnAnalyticApproach,CambridgeUniversityPress,Cambridge,2008. [12]Mattila,P.:GeometryofSetandMeasuresinEuclideanSpaces,CambridgeUniversityPress,Cambridge,1995.
  • [13] RogerA.J.:AdvancedEuclideanGeometry,DoverPublications,INC,NewYork,1960.
  • [14]Musielak,Z.E.,Fry,J.L.:GeneraldynamicalequationsforfreeparticlesandtheirGalileaninvariance,IntJTheorPhys,48,1194-1202(2009).
  • [15] Godunov,S.K.,Gordienko,V.M.:ComplicatedstructuresofGalilean-invariantconservationlaws,JournalofAppliedMechanicsandTechnical Physics, 43, No. 2, 175-189,(2002).
  • [16] W.W,H.,Havas,P.:GeneralizedGalilei-invariantclassicalmechanics,InternationalJournalofModernPhysicsA20,No.18.,4259-4289(2005).
  • [17]Karger,A.:KinematicgeometryinndimensionalEuclideanandsphericalspace,CzechoslovakMathematicalJournal,22,No.1,83–107(1972).

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

References

  • [1] Aripov R. and Khadjiev D.:The complete system of global differential and integral invariants of a curve in Euclidean geometry, Izvestiya Vuzov, Ser. Mathematics, 542, 1-14 (2007).(Russian). (English translation) Aripov R. and Khadzhiev D., Russian Mathematics (Iz VUZ), 2007, Vol. 51, No. 7, pp.1-14.
  • [2] BergerM.:Geometry I, Springer-Verlag,Berlin,Heidelberg,1987.
  • [3] ElleryB.G.:Foundations of Euclidean and Non-Euclidean Geometry,HoltRinehartand WinstonINC,NewYork,1968.
  • [4] Marvin,Y.G.:EuclideanandNon-EuclideanGeometries,W.H.FreemanandCompany,NewYork,1993.
  • [5] Ho ̋ferR.:m-pointinvariantsofrealgeometries,BeitrageAlgebraGeom,40,261-266(1999).
  • [6]O ̋ren I.,KhadjievD.and Peksen O.:Identificationsofpathsandcurvesundertheplanesimilaritytransformationsandtheirapplicationsto mechanics, Journal of Geometry and Physics, 151, (2020).
  • [7]KhadjievD.:CompletesystemsofdifferentialinvariantsofvectorfieldsinaEuclideanspace,TurkishJournalofMathematics,34,543-559(2010).
  • [8] KhadjievD.,O ̋renI.andPeks ̧enO ̋.:Globalinvariantsofpathsandcurvesforthegroupofalllinearsimilaritiesinthetwo-dimensionalEuclidean space, International Journal of Geometric Methods in Modern Physics, 15, No. 6, (2018).
  • [9] Khadjiev D.:Ayupov Sh. and Beshimov G.:Complete systems of invariants of m-tuples for fundamental groups of the two-dimensional Euclidean space, Uzbek Mathematical Journal, 1,71-98 (2020,).
  • [10] KhadjievD.,BekbaevU.,AripovR.:Onequivalenceofvector valuedmaps,arXiv:2005.08707v1[mathGM]13May2020.
  • [11] PatricJ.R.:EuclideanandNon-EclideanGeometry,AnAnalyticApproach,CambridgeUniversityPress,Cambridge,2008. [12]Mattila,P.:GeometryofSetandMeasuresinEuclideanSpaces,CambridgeUniversityPress,Cambridge,1995.
  • [13] RogerA.J.:AdvancedEuclideanGeometry,DoverPublications,INC,NewYork,1960.
  • [14]Musielak,Z.E.,Fry,J.L.:GeneraldynamicalequationsforfreeparticlesandtheirGalileaninvariance,IntJTheorPhys,48,1194-1202(2009).
  • [15] Godunov,S.K.,Gordienko,V.M.:ComplicatedstructuresofGalilean-invariantconservationlaws,JournalofAppliedMechanicsandTechnical Physics, 43, No. 2, 175-189,(2002).
  • [16] W.W,H.,Havas,P.:GeneralizedGalilei-invariantclassicalmechanics,InternationalJournalofModernPhysicsA20,No.18.,4259-4289(2005).
  • [17]Karger,A.:KinematicgeometryinndimensionalEuclideanandsphericalspace,CzechoslovakMathematicalJournal,22,No.1,83–107(1972).
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Djavvat Khadjiev 0000-0001-7056-5662

İdris Ören 0000-0003-2716-3945

Gayrat Beshimov 0000-0002-5394-2179

Early Pub Date July 23, 2022
Publication Date October 31, 2022
Acceptance Date October 28, 2022
Published in Issue Year 2022 Volume: 15 Issue: 2

Cite

APA Khadjiev, D., Ören, İ., & Beshimov, G. (2022). Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space. International Electronic Journal of Geometry, 15(2), 334-342. https://doi.org/10.36890/iejg.1091348
AMA Khadjiev D, Ören İ, Beshimov G. Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space. Int. Electron. J. Geom. October 2022;15(2):334-342. doi:10.36890/iejg.1091348
Chicago Khadjiev, Djavvat, İdris Ören, and Gayrat Beshimov. “Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space”. International Electronic Journal of Geometry 15, no. 2 (October 2022): 334-42. https://doi.org/10.36890/iejg.1091348.
EndNote Khadjiev D, Ören İ, Beshimov G (October 1, 2022) Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space. International Electronic Journal of Geometry 15 2 334–342.
IEEE D. Khadjiev, İ. Ören, and G. Beshimov, “Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space”, Int. Electron. J. Geom., vol. 15, no. 2, pp. 334–342, 2022, doi: 10.36890/iejg.1091348.
ISNAD Khadjiev, Djavvat et al. “Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space”. International Electronic Journal of Geometry 15/2 (October 2022), 334-342. https://doi.org/10.36890/iejg.1091348.
JAMA Khadjiev D, Ören İ, Beshimov G. Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space. Int. Electron. J. Geom. 2022;15:334–342.
MLA Khadjiev, Djavvat et al. “Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space”. International Electronic Journal of Geometry, vol. 15, no. 2, 2022, pp. 334-42, doi:10.36890/iejg.1091348.
Vancouver Khadjiev D, Ören İ, Beshimov G. Complete Systems of Galileo Invariants of a Motion of Parametric Figure in the Three Dimensional Euclidean Space. Int. Electron. J. Geom. 2022;15(2):334-42.
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