Robust integration of dual quaternion approaches, magnetic offsets and screw motion

Abstract

In this study, the dual magnetic curves of the corresponding flux surfaces are determined, and the use of these dual curves enables the definition of magnetic offsets. The kinematic properties of these curves are explored, emphasizing their role in describing the motion and transformations of the flux surfaces. The integral invariants of the flux surfaces and developable are investigated by the utilization of the dual magnetic angle between dual magnetic curves. Additionally, we identify connections between Mannheim offsets and spherical images associated with dual quaternions. Furthermore, the study utilizes dual quaternions to perform a geometric and kinematic analysis of magnetic curves and screw motion, providing a comprehensive framework to link magnetic geometry and kinematic motion.