Time Scale Approach to One Parameter Plane Motion by Complex Numbers

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.

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Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Samanci, H. and Caliskan, A. (2015) Time Scale Approach to One Parameter Plane Motion by Complex Numbers. Advances in Pure Mathematics, 5, 42-50. doi: 10.4236/apm.2015.51005.

 [1] Aulbach, B. and Hilger, S. (1990) Linear Dynamic Processes within Homogeneous Time Scale. Nonlinear Dynamics and Quantum Dynamical System, Berlin Akademie Verlag, 9-20. [2] Bohner, M. and Peterson, A. (2003) Advances in Dynamic Equations on Time Scales, Birkh User. [3] Bohner, M. and Peterson, A. (2001) Dynamic Equations on Time Scales, An Introduction with Applications, Birkh User. [4] Bohner, M. and Guseyinov, G. (2005) An introduction to Complex Functions on Products of Two Time Scales. Journal of Difference Equations and Applications, 12. [5] Bottema, O. and Roth, B. (1990) Theoretical Kinematics. Dover Publications, Mineola. [6] Blaschke, W. (1960) Kinematik und Quaternionen. Mathematische Monographien. Springer, Berlin. [7] Blaschke, W. and Muller, H.R. (1956) Ebene Kinematik, Oldenbourg, Munchen.