الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
” Many fields of science and philosophy attempt to explain some of the universe’s phenomena where each field relates to the other to achieve its existence. Physics and mathematics, for example, are used to examine some phenomena, beginning with axioms and hypotheses passing through observations, data analysis and experiments to arrive at useful and usable logical results. In recent years, there has been much research activity concerning the analysis of the motion of particles along a curve and the geometric properties of surfaces in 3D Euclidean space E³. To a large extent, this is due to the realization that differential geometry is important in applications. New applications that involve differential geometry continue to arise with increasing frequency in the explanation of diverse phenomena in physics, biology, ecology and physiology. The main objective of this thesis is to shed light on some physical concepts and their equations from the perspective of differential geometry, through studying the kinematics properties or the geometric properties of these concepts and equations by using different and improved moving frames. We discussed, in detail, some kinematics properties of a particle and some geometric properties of a Hasimoto surface in 3D Euclidean space E³. Specifically, the topics dealt with include the following: obtaining an alternative resolution of the acceleration vector, the jerk vector and the snap vector; studying the geometry of solutions of the vortex filament equation (VFE). Moreover, we will use some new moving frames for studying the kinematics properties and the geometric properties, including the following: Modified orthogonal frame. Quasi orthonormal frame.