One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane 详细信息    查看全文

• 作者：Nurten Gürses ; Mücahit Akbiyik ; Salim Yüce
• 关键词：Generalized complex number plane ; One ; parameter planar homothetic motion ; Kinematics ; Euler ; Savary formula
• 刊名：Advances in Applied Clifford Algebras
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：26
• 期：1
• 页码：115-136
• 全文大小：732 KB
• 参考文献：1.Alfsmann, D.: On families of 2N dimensional Hypercomplex Algebras suitable for digital signal Processing. In: Proceedigs of EURASIP 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy (2006)
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  4.Akbıyık, M., Yüce, S.: One-parameter homothetic motion on the galilean plane (Submitted)
  5.Akbıyık, M., Yüce, S.: The moving coordinate system and Euler-Savary’s formula for the one parameter motions on Galilean (Isotropic) plane. Int. J. Math. Comb. (2), 88–105 (2015)
  6.Akbıyık, M., Yüce, S.: Euler Savary’s formula on Galilean plane (Submitted)
  7.Aytun, I.: Euler-Savary formula for one-parameter Lorentzian plane motion and its Lorentzian geometrical interpretation. Master Thesis, Celal Bayar University Graduate School of Natural and Applied Sciences (2002)
  8.Beggs, J.S.: Kinematics, Taylor and Francis. p. 1 (1983)
  9.Blaschke, W., Müller, H.R.: Ebene Kinematik. Verlag Oldenbourg, München (1956)
  10.Biewener, A.: Animal Locomotion, Oxford University Press (2003)
  11.Buckley R., Whitfield E.V.: The Euler-Savary formula. Math Gaz. 33(306), 297–299 (1949)CrossRef
  12.Catoni, F., Boccaletti, D., Cannata, R., Catoni, V., Nichelatti, E., and Zampetti, P.: The mathematics of Minkowski space-time and an introduction to commutative hypercomplex numbers. Birkh auser Verlag, Basel (2008)
  13.Catoni F., Cannata R., Catoni V., Zampetti P.: Hyperbolic trigonometry in two-dimensional space-time geometry. N. Cim B 118, 475–491 (2003)ADS MathSciNet
  14.Dimentberg, F.M.: The screw calculus and its applications in mechanics, Foreign Technology Division translation FTD-HT-23-1632-67 (1965)
  15.Dimentberg F.M.: The method of screws and calculus of screws applied to the theory of three dimensional mechanisms. Adv. Mech. 1(3–4), 91–106 (1978)MathSciNet
  16.Dooner D.B., Griffis M.W.: On the spatial Euler-Savary equations for envelopes. J. Mech. Des. 129(8), 865–875 (2007)CrossRef
  17.Ergüt M., Aydın A.P., Bildik N.: The geometry of the canonical relative system and the one-parameter motions in 2-dimensional lorentzian space. J. Fırat Univ. 3(1), 113–122 (1988)
  18.Ergin A.A.: On the one-parameter Lorentzian motion. Commun. Fac. Sci. Univ. Ankara. Ser. A 40, 59–66 (1991)MathSciNet MATH
  19.Ergin A.A.: Three Lorentzian planes moving with respect to one another and pole points. Commun. Fac. Sci.Univ. Ankara. Ser. A 41, 79–84 (1992)MathSciNet MATH
  20.Ersoy S., Akyiğit M.: One-parameter homothetic motion in the hyperbolic plane and Euler-Savary formula. Commun. Fac. Adv. Appl. Clifford Algebras 21, 297–313 (2011)CrossRef MATH
  21.Es, H.: Motions and nine different geometry. Ph.D. Thesis, Ankara University Graduate School of Natural and Applied Sciences (2003)
  22.Fjelstad P.: Extending special relativity via the perplex numbers. Am. J. Phys. 54(5), 416–422 (1986)CrossRef ADS MathSciNet
  23.Fjelstad P., Gal S.G.: n-dimensional hyperbolic complex numbers. Adv. Appl. Clifford Algebra 8(1), 47–68 (1998)CrossRef MathSciNet MATH
  24.Fjelstad P., Gal S.G.: Two-dimensional geometries, topologies, trigonometries and physics generated by complex-type numbers. Adv. Appl. Clifford Algebra 11(1), 81–107 (2001)CrossRef MathSciNet MATH
  25.Gürses, N.B., Yüce, S.: One-parameter planar motions in affine cayley-klein planes. Eur. J. Pure Appl. Math. 7(3), 335–342 (2014)
  26.Gürses, N., Yüce, S.: On the moving coordinate system and Euler-Savary formula in affine Cayley–Klein planes, Submitted
  27.Gürses, N., Yüce, S.: One-parameter planar motions in generalized complex number plane \({\mathbb{C}_{J}}\) Adv. Appl. Clifford Algebras, doi:10.​1007/​s00006-015-0530-4
  28.Gromov N.A., Moskaliuk S.S.: Classication of transitions between groups in Cayley–Klein spaces and kinematic groups. Hadronic J 19(4), 407–435 (1996)MathSciNet MATH
  29.Gromov N.A., Kuratov V.V.: Possible quantum kinematics. J. Math. Phys. 47, 1 (2006)CrossRef MathSciNet
  30.Hacisalihoğlu H.: On the rolling of one curve or surface upon another. Proc. R. Ir Acad. Sect. A: Math. Phys. Sci. 71, 13–17 (1971)
  31.Harkin, A.A., Harkin, J.B.: Geometry of Generalized Complex Numbers. Math. Mag. 77, 2 (2014)
  32.Helzer G.: Special relativity with acceleration. Am. Math. Month. 107(3), 219–237 (2000)CrossRef MathSciNet MATH
  33.Herranz, F.J., Santader, M.: Homogeneous phase spaces: the Cayley–Klein framework. (1997). arXiv:​physics/​9702030v1
  34.Ikawa T.: Euler-Savarys formula on Minkowski geometry. Balkan J. Geom. Appl. 8(2), 31–36 (2003)MathSciNet MATH
  35.Ito N., Takahashi K.: Extension of the Euler-Savary equation to hypoid gears. JSME Int. J. Ser. C. Mech Syst. 42(1), 218–224 (1999)CrossRef ADS
  36.Klein, F.: Über die sogenante nicht-Euklidische Geometrie. Gesammelte Math. Abh. 254–305 (1921)
  37.Klein, F.: Vorlesungen über nicht-Euklidische Geometrie. Springer, Berlin (1928)
  38.Kisil, V.V.: Geometry of möbius transformations: eliptic, parabolic and hyperbolic actions of \({S{L_2} (\mathbb{R})}\) . Imperial College Press, London (2012)
  39.Köse Ö: Kinematic differential geometry of a rigid body in spatial motion using dual vector calculus: Part-I. Appl. Math. Comput. 183(1), 17–29 (2006)CrossRef MathSciNet MATH
  40.Kuruoğlu N., Tutar A., Düldül M.: On the moving coordinate system on the complex plane and pole points. Bull. Pure Appl. Sci. 20(1), 1–6 (2001)MathSciNet MATH
  41.Kuruoğlu N., Tutar A., Düldül M.: On the 1-parameter homothetic motions on the complex plane. Int. J. Appl. Math. 6(4), 439–447 (2001)MathSciNet MATH
  42.Masal M., Ersoy S., Güngör M.A.: Euler-Savary formula for the homothetic motion in the complex plane \({\mathbb{C}}\) . Ain Shams Eng. J. 5, 305–308 (2014)CrossRef
  43.Masal M., Tosun M., Pirdal A.Z.: Euler Savary formula for the one parameter motions in the complex plane \({\mathbb{C}}\) . Int. J. Phys. Sci. 5(1), 006–010 (2010)
  44.McRae, A.S.: Clifford fibrations and possible kinematics. Symmetry, Integrability Geom: Methods Appl 5 (072) (2009)
  45.Müller H.R.: Verallgemeinerung einer formel von Steiner. Abh. d. Brschw. Wiss. Ges 24, 107– (1978)
  46.Pennock, G.R., Raje, N.N.: Curvature theory for the double flier eight-bar linkage Mech. Theory 39, 665–679 (2004)
  47.Pennestri E., Stefanelli R.: Linear algebra and numerical algorithms using dual numbers. Multibody Syst. Dyn. 18(3), 323–344 (2007)CrossRef MathSciNet
  48.Röschel O.: Zur Kinematik der isotropen Ebene. J. Geom. 21, 146–156 (1983)CrossRef MathSciNet MATH
  49.Röschel, O.: Die Geometrie des Galileischen Raumes, Habilitationsschrift, Institut für Math. und Angew. Geometrie, Leoben (1984)
  50.Röschel O.: Zur Kinematik der isotropen Ebene II. J. Geom. 24, 112–122 (1985)CrossRef MathSciNet MATH
  51.Rochon D., Shapiro M.: On algebraic properties of bicomplex and hyperbolic numbers. Anal. Univ. Oradea, Fasc. Math. 11, 71–110 (2004)MathSciNet MATH
  52.Sanjuan, M.A.F.: Group contraction and nine Cayley–Klein geometries. Int. J. Theor. Phys. 23(1) (1984)
  53.Sandor G.N., Arthur G.E., Raghavacharyulu E.: Double valued solutions of the Euler-Savary equation and its counterpart in Bobillier’s construction. Mech. Mach. Theory 20(2), 145–178 (1985)CrossRef
  54.Salgado, R.: Space-time trigonometry. AAPT Topical Conference: Teaching General Relativity to Undergraduates, AAPT Summer Meeting, Syrauce University, NY, July 20–21, 22–26 (2006)
  55.Spirova M.: Propellers in affine Cayley–Klein planes. J. Geom. 93, 164–167 (2009)CrossRef MathSciNet MATH
  56.Study, E.: Geometrie der Dynamen. Verlag Teubner, Leipzig (1903)
  57.Sobczyk G.: The hyperbolic number plane. Coll. Math. J. 26(4), 268–280 (1995)CrossRef
  58.Sandor G.N., Xu Y., Weng T.-C.: A graphical method for solving the Euler-Savary equation. Mech. Mach. Theory 25(2),141–147 (1990)CrossRef
  59.Tutar A., Kuruoğlu N.: On the one-parameter homothetic motions on the Lorentzian plane. Bull. Pure Appl. Sci. 18(2), 333–340 (1999)MathSciNet
  60.Veldkamp G.R.: On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics. Mech. Mach. Theory 11(2), 141–156 (1976)CrossRef
  61.Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press. Chapter 1 (1904)
  62.Wright, T.W.: Elements of Mechanics Including Kinematics, Kinetics and Statics. E and FN Spon. Chapter 1, (1896)
  63.Yaglom, I.M.: Complex numbers in geometry. Academic Press, New York (1968)
  64.Yüce S., Kuruoğlu N.: One-parameter plane hyperbolic motions. Adv. Appl. Clifford alg 18, 279–285 (2008)CrossRef MATH
  65.Yaglom, I.M.: A simple non-Euclidean geometry and its Physical Basis. Springer, New York (1979)
  66.Yüce S., Akar M.: Dual plane and kinematics. Chiang Mai J. Sci. 41(2), 463–469 (2014)MathSciNet
  
• 作者单位：Nurten Gürses (1)
  Mücahit Akbiyik (1)
  Salim Yüce (1)
  
  1. Department of Mathematics, Faculty of Arts and Sciences, Yildiz Technical University, Esenler, Istanbul, 34220, Turkey
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Mathematical Methods in Physics
  Mathematical and Computational Physics
  Applications of Mathematics
  Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-4909

文摘

In this paper, we introduce one-parameter homothetic motions in the generalized complex number plane (\({\mathfrak{p}}\)-complex plane) $$\mathbb{C}_{J}=\left\{x+Jy:\,\,\, x,y \in \mathbb{R},\quad J^2=\mathfrak{p},\quad \mathfrak{p} \in \{-1,0,1\} \right\} \subset \mathbb{C}_\mathfrak{p}$$where $$\mathbb{C}_\mathfrak{p}=\{x+Jy:\,\,\, x,y \in \mathbb{R}, \quad J^2=\mathfrak{p}\}$$such that \({-\infty < \mathfrak{p} < \infty}\). The velocities, accelerations and pole points of the motion are analysed. Moreover, three generalized complex number planes, of which two are moving and the other one is fixed, are considered and a canonical relative system for one-parameter planar homothetic motion in \({\mathbb{C}_{J}}\) is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, during the one-parameter homothetic motions, is obtained with the aim of this canonical relative system. Keywords Generalized complex number plane One-parameter planar homothetic motion Kinematics Euler-Savary formula Mathematics Subject Classification 53A17 53A35 53A40 Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (66) References1.Alfsmann, D.: On families of 2N dimensional Hypercomplex Algebras suitable for digital signal Processing. In: Proceedigs of EURASIP 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy (2006)2.Alexander J.C., Maddocks J.H.: On the maneuvering of vehicles. SIAM J. Appl. Math 48(1), 38–52 (1988)CrossRefMathSciNetMATH3.Akar M., Yüce S., Kuruoğlu N.: One-parameter planar motion in the galilean plane. Int. Electron. J. Geom. (IEJG) 6(1), 79–88 (2013)MATH4.Akbıyık, M., Yüce, S.: One-parameter homothetic motion on the galilean plane (Submitted)5.Akbıyık, M., Yüce, S.: The moving coordinate system and Euler-Savary’s formula for the one parameter motions on Galilean (Isotropic) plane. Int. J. Math. Comb. (2), 88–105 (2015)6.Akbıyık, M., Yüce, S.: Euler Savary’s formula on Galilean plane (Submitted)7.Aytun, I.: Euler-Savary formula for one-parameter Lorentzian plane motion and its Lorentzian geometrical interpretation. Master Thesis, Celal Bayar University Graduate School of Natural and Applied Sciences (2002)8.Beggs, J.S.: Kinematics, Taylor and Francis. p. 1 (1983)9.Blaschke, W., Müller, H.R.: Ebene Kinematik. Verlag Oldenbourg, München (1956)10.Biewener, A.: Animal Locomotion, Oxford University Press (2003)11.Buckley R., Whitfield E.V.: The Euler-Savary formula. Math Gaz. 33(306), 297–299 (1949)CrossRef12.Catoni, F., Boccaletti, D., Cannata, R., Catoni, V., Nichelatti, E., and Zampetti, P.: The mathematics of Minkowski space-time and an introduction to commutative hypercomplex numbers. Birkh auser Verlag, Basel (2008)13.Catoni F., Cannata R., Catoni V., Zampetti P.: Hyperbolic trigonometry in two-dimensional space-time geometry. N. Cim B 118, 475–491 (2003)ADSMathSciNet14.Dimentberg, F.M.: The screw calculus and its applications in mechanics, Foreign Technology Division translation FTD-HT-23-1632-67 (1965)15.Dimentberg F.M.: The method of screws and calculus of screws applied to the theory of three dimensional mechanisms. Adv. Mech. 1(3–4), 91–106 (1978)MathSciNet16.Dooner D.B., Griffis M.W.: On the spatial Euler-Savary equations for envelopes. J. Mech. Des. 129(8), 865–875 (2007)CrossRef17.Ergüt M., Aydın A.P., Bildik N.: The geometry of the canonical relative system and the one-parameter motions in 2-dimensional lorentzian space. J. Fırat Univ. 3(1), 113–122 (1988)18.Ergin A.A.: On the one-parameter Lorentzian motion. Commun. Fac. Sci. Univ. Ankara. Ser. A 40, 59–66 (1991)MathSciNetMATH19.Ergin A.A.: Three Lorentzian planes moving with respect to one another and pole points. Commun. Fac. Sci.Univ. Ankara. Ser. A 41, 79–84 (1992)MathSciNetMATH20.Ersoy S., Akyiğit M.: One-parameter homothetic motion in the hyperbolic plane and Euler-Savary formula. Commun. Fac. Adv. Appl. Clifford Algebras 21, 297–313 (2011)CrossRefMATH21.Es, H.: Motions and nine different geometry. Ph.D. Thesis, Ankara University Graduate School of Natural and Applied Sciences (2003)22.Fjelstad P.: Extending special relativity via the perplex numbers. Am. J. Phys. 54(5), 416–422 (1986)CrossRefADSMathSciNet23.Fjelstad P., Gal S.G.: n-dimensional hyperbolic complex numbers. Adv. Appl. Clifford Algebra 8(1), 47–68 (1998)CrossRefMathSciNetMATH24.Fjelstad P., Gal S.G.: Two-dimensional geometries, topologies, trigonometries and physics generated by complex-type numbers. Adv. Appl. Clifford Algebra 11(1), 81–107 (2001)CrossRefMathSciNetMATH25.Gürses, N.B., Yüce, S.: One-parameter planar motions in affine cayley-klein planes. Eur. J. Pure Appl. Math. 7(3), 335–342 (2014)26.Gürses, N., Yüce, S.: On the moving coordinate system and Euler-Savary formula in affine Cayley–Klein planes, Submitted27.Gürses, N., Yüce, S.: One-parameter planar motions in generalized complex number plane \({\mathbb{C}_{J}}\) Adv. Appl. Clifford Algebras, doi:10.​1007/​s00006-015-0530-4 28.Gromov N.A., Moskaliuk S.S.: Classication of transitions between groups in Cayley–Klein spaces and kinematic groups. Hadronic J 19(4), 407–435 (1996)MathSciNetMATH29.Gromov N.A., Kuratov V.V.: Possible quantum kinematics. J. Math. Phys. 47, 1 (2006)CrossRefMathSciNet30.Hacisalihoğlu H.: On the rolling of one curve or surface upon another. Proc. R. Ir Acad. Sect. A: Math. Phys. Sci. 71, 13–17 (1971)31.Harkin, A.A., Harkin, J.B.: Geometry of Generalized Complex Numbers. Math. Mag. 77, 2 (2014)32.Helzer G.: Special relativity with acceleration. Am. Math. Month. 107(3), 219–237 (2000)CrossRefMathSciNetMATH33.Herranz, F.J., Santader, M.: Homogeneous phase spaces: the Cayley–Klein framework. (1997). arXiv:​physics/​9702030v1 34.Ikawa T.: Euler-Savarys formula on Minkowski geometry. Balkan J. Geom. Appl. 8(2), 31–36 (2003)MathSciNetMATH35.Ito N., Takahashi K.: Extension of the Euler-Savary equation to hypoid gears. JSME Int. J. Ser. C. Mech Syst. 42(1), 218–224 (1999)CrossRefADS36.Klein, F.: Über die sogenante nicht-Euklidische Geometrie. Gesammelte Math. Abh. 254–305 (1921)37.Klein, F.: Vorlesungen über nicht-Euklidische Geometrie. Springer, Berlin (1928)38.Kisil, V.V.: Geometry of möbius transformations: eliptic, parabolic and hyperbolic actions of \({S{L_2} (\mathbb{R})}\). Imperial College Press, London (2012)39.Köse Ö: Kinematic differential geometry of a rigid body in spatial motion using dual vector calculus: Part-I. Appl. Math. Comput. 183(1), 17–29 (2006)CrossRefMathSciNetMATH40.Kuruoğlu N., Tutar A., Düldül M.: On the moving coordinate system on the complex plane and pole points. Bull. Pure Appl. Sci. 20(1), 1–6 (2001)MathSciNetMATH41.Kuruoğlu N., Tutar A., Düldül M.: On the 1-parameter homothetic motions on the complex plane. Int. J. Appl. Math. 6(4), 439–447 (2001)MathSciNetMATH42.Masal M., Ersoy S., Güngör M.A.: Euler-Savary formula for the homothetic motion in the complex plane \({\mathbb{C}}\). Ain Shams Eng. J. 5, 305–308 (2014)CrossRef43.Masal M., Tosun M., Pirdal A.Z.: Euler Savary formula for the one parameter motions in the complex plane \({\mathbb{C}}\). Int. J. Phys. Sci. 5(1), 006–010 (2010)44.McRae, A.S.: Clifford fibrations and possible kinematics. Symmetry, Integrability Geom: Methods Appl 5 (072) (2009)45.Müller H.R.: Verallgemeinerung einer formel von Steiner. Abh. d. Brschw. Wiss. Ges 24, 107– (1978)46.Pennock, G.R., Raje, N.N.: Curvature theory for the double flier eight-bar linkage Mech. Theory 39, 665–679 (2004)47.Pennestri E., Stefanelli R.: Linear algebra and numerical algorithms using dual numbers. Multibody Syst. Dyn. 18(3), 323–344 (2007)CrossRefMathSciNet48.Röschel O.: Zur Kinematik der isotropen Ebene. J. Geom. 21, 146–156 (1983)CrossRefMathSciNetMATH49.Röschel, O.: Die Geometrie des Galileischen Raumes, Habilitationsschrift, Institut für Math. und Angew. Geometrie, Leoben (1984)50.Röschel O.: Zur Kinematik der isotropen Ebene II. J. Geom. 24, 112–122 (1985)CrossRefMathSciNetMATH51.Rochon D., Shapiro M.: On algebraic properties of bicomplex and hyperbolic numbers. Anal. Univ. Oradea, Fasc. Math. 11, 71–110 (2004)MathSciNetMATH52.Sanjuan, M.A.F.: Group contraction and nine Cayley–Klein geometries. Int. J. Theor. Phys. 23(1) (1984)53.Sandor G.N., Arthur G.E., Raghavacharyulu E.: Double valued solutions of the Euler-Savary equation and its counterpart in Bobillier’s construction. Mech. Mach. Theory 20(2), 145–178 (1985)CrossRef54.Salgado, R.: Space-time trigonometry. AAPT Topical Conference: Teaching General Relativity to Undergraduates, AAPT Summer Meeting, Syrauce University, NY, July 20–21, 22–26 (2006)55.Spirova M.: Propellers in affine Cayley–Klein planes. J. Geom. 93, 164–167 (2009)CrossRefMathSciNetMATH56.Study, E.: Geometrie der Dynamen. Verlag Teubner, Leipzig (1903)57.Sobczyk G.: The hyperbolic number plane. Coll. Math. J. 26(4), 268–280 (1995)CrossRef58.Sandor G.N., Xu Y., Weng T.-C.: A graphical method for solving the Euler-Savary equation. Mech. Mach. Theory 25(2),141–147 (1990)CrossRef59.Tutar A., Kuruoğlu N.: On the one-parameter homothetic motions on the Lorentzian plane. Bull. Pure Appl. Sci. 18(2), 333–340 (1999)MathSciNet60.Veldkamp G.R.: On the use of dual numbers, vectors and matrices in instantaneous, spatial kinematics. Mech. Mach. Theory 11(2), 141–156 (1976)CrossRef61.Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press. Chapter 1 (1904)62.Wright, T.W.: Elements of Mechanics Including Kinematics, Kinetics and Statics. E and FN Spon. Chapter 1, (1896)63.Yaglom, I.M.: Complex numbers in geometry. Academic Press, New York (1968)64.Yüce S., Kuruoğlu N.: One-parameter plane hyperbolic motions. Adv. Appl. Clifford alg 18, 279–285 (2008)CrossRefMATH65.Yaglom, I.M.: A simple non-Euclidean geometry and its Physical Basis. Springer, New York (1979)66.Yüce S., Akar M.: Dual plane and kinematics. Chiang Mai J. Sci. 41(2), 463–469 (2014)MathSciNet About this Article Title One-Parameter Homothetic Motions and Euler-Savary Formula in Generalized Complex Number Plane \({\mathbb{C}_{J}}\) Journal Advances in Applied Clifford Algebras Volume 26, Issue 1 , pp 115-136 Cover Date2016-03 DOI 10.1007/s00006-015-0598-x Print ISSN 0188-7009 Online ISSN 1661-4909 Publisher Springer International Publishing Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Applications of Mathematics Physics, general Keywords 53A17 53A35 53A40 Generalized complex number plane One-parameter planar homothetic motion Kinematics Euler-Savary formula Industry Sectors Aerospace Electronics IT & Software Telecommunications Authors Nurten Gürses (1) Mücahit Akbiyik (1) Salim Yüce (1) Author Affiliations 1. Department of Mathematics, Faculty of Arts and Sciences, Yildiz Technical University, Esenler, Istanbul, 34220, Turkey Continue reading... To view the rest of this content please follow the download PDF link above.