Abstract
Geometric algebra is a useful tool to overcome some problems in kinematics. Thus, the geometric algebra has attracted the attention of many researchers. In this paper, quaternion operators on curves and surfaces in Euclidean 3-space are defined by using geometric algebra. These operators generate the curves or the surfaces from the points, curves or surfaces. Using quaternion operators, we obtain motions that have orbits along the generated curve or surface. Also, these motions are expressed as 1-parameter or 2-parameter homothetic motions.
Highlights
Kinematics is a research field of geometry to describe the motion of points, lines and other geometric objects
We define quaternion operators using geometric algebra and classify these operators according to their orbits
Quaternion operator with curve orbit generates a curve from a point or a curve
Summary
Kinematics is a research field of geometry to describe the motion of points, lines and other geometric objects. Some problems and difficulties have been encountered in modeling of the mathematics of 3-dimensional (3D) kinematics These difficulties have been tried to overcome by using quaternions. Curves, surfaces, quaternions, rotation matrices, homothetic motions. Some surfaces were obtained by quaternions or homothetic motions in [9,10,11,12,13,14,15]. We define quaternion operators using curves and surfaces in E3. These operators have allowed us to obtain a quaternionic or a homothetic motion on each curve and surface in E3 These motions have orbits along curves or surfaces. Quaternion operator with curve orbit converts a point to a curve or a curve to a curve This operator is expressed as 1-parameter homothetic motion. Quaternion operator with surface orbit is expressed as 2-parameter homothetic motion.
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