%0 Journal Article
%T Time Scale Approach to One Parameter Plane Motion by Complex Numbers
%A Hatice Kusak Samanci
%A Ali Caliskan
%J Advances in Pure Mathematics
%P 42-50
%@ 2160-0384
%D 2015
%I Scientific Research Publishing
%R 10.4236/apm.2015.51005
%X <p style=\"text-align:justify;\">
	<span style=\"font-size:10px;font-family:Verdana;line-height:2;\">This paper presents building one-parameter motion by complex numbers on a
time scale. Firstly, we assumed that </span><b><i><span style=\"font-family:Verdana;font-size:10px;line-height:2;\">E</span></i></b><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"> </span><span style=\"font-size:10px;font-family:Verdana;line-height:2;\">and </span><b><i><span style=\"font-size:10px;font-family:Verdana;line-height:2;\">E</span></i></b><span style=\"font-size:10px;font-family:Verdana;line-height:2;\">กไ</span><span style=\"font-size:10px;font-family:Verdana;line-height:2;\"> were moving in a fixed
time scale complex plane and {0, e<sub>1</sub></span>,e<sub>2<i></i></sub>} and {0', <span style=\"font-family:Verdana;line-height:20px;text-align:justify;white-space:normal;\">e'<sub>1<i></i></sub>,e'<sub>2<i></i></sub></span>} &nbsp;were their orthonormal frames, respectively. By
using complex numbers, we investigated the delta calculus equations of the motion
on<span style=\"font-family:Verdana;font-size:10px;line-height:2;\"> T</span><span style=\"font-size:10px;font-family:Verdana;line-height:2;\">. Secondly, we gave
the velocities and their union rule on the time scale. Finally, by using the delta-derivative,
we got interesting results and theorems for the instantaneous rotation pole and
the pole curves (trajectory). In kinematics, investigating one-parameter motion
by complex numbers is important for simplifying motion calculation. In this study,
our aim is to obtain an equation of motion by using complex numbers on the time
scale.</span> 
</p>
%K Complex Numbers
%K Kinematic
%K Time Scales
%K Pole Curve
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53475