Plane C
jNurten Gürses1, Salim Yüce2 and Mücahit Akbıyık3
1Faculty of Arts and Sciences, Department of Mathematics, Yildiz Technical University, Esenler, Istanbul, 34220
nbayrak@yildiz.edu.tr
2Faculty of Arts and Sciences, Department of Mathematics, Yildiz Technical University, Esenler, Istanbul, 34220
sayuce@yildiz.edu.tr
3Faculty of Arts and Sciences, Department of Mathematics, Yildiz Technical University, Esenler, Istanbul, 34220
makbiyik@yildiz.edu.tr
Abstract
In this study, we firstly give the basic notations of the generalized complex number plane (p-complex plane) Cp. Then, we introduce the one-parameter planar homothetic motions
CJ/C′J in p-complex plane CJ such that CJ ⊂ Cp by examining the velocities, accelerations and pole points. Besides, we discuss the relations between absolute, relative, sliding velocities (accelerations) and pole curves under these motions. 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 CJ 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.
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