TITLE:
Time Scale Approach to One Parameter Plane Motion by Complex Numbers
AUTHORS:
Hatice Kusak Samanci, Ali Caliskan
KEYWORDS:
Complex Numbers, Kinematic, Time Scales, Pole Curve
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.1,
January
23,
2015
ABSTRACT: This paper presents building one-parameter motion by complex numbers on a
time scale. Firstly, we assumed that E and E′ were moving in a fixed
time scale complex plane and {0, e1,e2} and {0', e'1,e'2} were their orthonormal frames, respectively. By
using complex numbers, we investigated the delta calculus equations of the motion
on T. 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.