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One-Parameter Planar Motions in Affine Cayley-Klein Planes

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2014

Key Words:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In 1956, W. Blaschke and H.R. Müller introduced the one-parameter planar motions and obtained the relation between absolute, relative, sliding velocities and accelerations in the Euclidean plane E2 [3]. A. A. Ergin [4] considering the Lorentzian plane L2, instead of the Euclidean plane E2, introduced the one-parameter planar motions in the Lorentzian plane L2 and also gave the relations between the velocities and accelerations in 1991. In addition to this, in 2013, M. Akar and S. Yüce [1] introduced the one-parameter motions in the Galilean plane G2 and gave same concepts stated above. In this paper, we will introduce one parameter planar motions in affine Cayley-Klein (CK) planes Pe and we will discuss the relations between absolute, relative, sliding velocities and accelerations.
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REFERENCES

References: 

[1] M. Akar, S. Yüce, and N. Kuruoğlu. One-Parameter Planar Motion in the Galilean Plane.
International Electronic Journal ofGeometry(IEJG), 6(1): 79-88, 2013.
[2] M. Akbıyık. Moving coordinate system and Euler Savary formula on Galilean plane. Master Thesis, Yıldız Technical University Graduate School of Natural and Applied Sciences,
2012.
[3] W. Blaschke and H.R. Müller. Ebene Kinematik. Verlag Oldenbourg, München, 1956.
[ 4] A. A. Ergin. On the one-parameter Lorentzian motion. Communications, FacultyofScience, University of Ankara, Series A 40, 59-66,1991.
[ 5 ] H. Es. Motions and Nine Different Geometry. PhD Thesis, Ankara University Graduate School of Natural and Applied Sciences, 2003.
REFERENCES
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[6] G. Helzer. Special Relativity with Acceleration, The American Mathematical Monthly, 107(3), 219-237, 2000.
[7] F. J. Herranz and M. Santader. Homogeneous Phase Spaces: The Cayley-Klein framework, http://arxiv. org/pdf/physics f9702030v1.pdf.
[8] F. Klein. Über die sogenante nicht-Euklidische Geometrie,Gesammelte Mathematische Ab-
handlungen, 254-305, 1921.
[9] F. Klein. Vorlesungen über nicht-Euklidische Geometrie, Springer, Berlin, 1928.
[10] R. Salgado. Space-Time Trigonometry. AAPT Topical Conference: Teaching General Relativity to Undergraduates, AAPT Summer Meeting, Syrauce University, NY, July 20-21,22-26.
2006.
[11] M. A. F. Sanjuan. Group Contraction and Nine Cayley-Klein Geometries, International Journal ofTheoretical Physics, 23(1), 1984.
[12] M. Spirova. Propellers in Affine Cayley-Klein Planes, Journal of Geometry. 93, 164-167,
2009.
[13] H. Urban. Über drei zwanglaufiggegeneinander bewegte Cayley/Klein-Ebenen. Geome-
triae Dedicata, 53:187-199, 1994.
[14] I. M. Yaglom. A simple non-Euclidean geometry and its Physical Basis. Springer-Verlag,
New York, 1979.

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