Paper Type |
Contributed Paper |
Title |
Dual Plane and Kinematics |
Author |
Salim Yüce* [a] and Mutlu Akar [a] |
Email |
sayuce@yildiz.edu.tr |
Abstract: Müller, H. R. [2], on the Euclidean plane , introduced the one-parameter planar motion and obtained the relation between absolute, relative, sliding velocities (and accelerations). Also, Müller, H. R. [6] provided the relation between the velocities (in the sense of Complex) under the one-parameter motion on the Complex plane .
Ergin, A. A. [4] considered the Lorentzian plane , instead of the Euclidean plane , and introduced the one-parameter planar motion on the Lorentzian plane and also gave the relations between both the velocities and the accelerations. Yüce, S. [12] introduced the relation between the velocities (in the sense of Hyperbolic) under the one-parameter motions on the Hyperbolic plane . Yüce, S. [1] considered the Galilean plane , instead of the Euclidean plane and Lorentzian plane , and introduced the one-parameter planar motion on the Galilean plane and also gave the relations between both the velocities and accelerations. In analogy with the Complex numbers and Hyperbolic numbers, a system of Dual numbers can be introduced: . Complex numbers are related to the Euclidean geometry, the Dual and Hyperbolic systems of numbers are related to the Galilean geometry and Lorentz (or Minkowski) geometry, respectively, [9,10]. In this paper, in analogy with Complex motions as given by Müller, H.R. [6] and Hyperbolic motions as given by Yüce, S. [12], one-parameter motion on the Dual plane are defined. Also the relations between absolute, relative, sliding velocities (and accelerations) and pole lines are discussed. |
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Start & End Page |
463 - 469 |
Received Date |
2011-12-13 |
Revised Date |
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Accepted Date |
2013-05-09 |
Full Text |
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Keyword |
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Volume |
Vol.41 No.2 (APRIL 2014) |
DOI |
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Citation |
Yüce S. and Akar M., Dual Plane and Kinematics, Chiang Mai J. Sci., 2014; 41(2): 463-469. |
SDGs |
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