New Applications on the Flows of Space-like curves specified by Normal acceleration in Minkowski Space ℝ²,¹

This paper investigates the kinematic motions of space-like and time-like curves specified by acceleration fields in Minkowski space ℝ²,¹. Through the motion, the relationship between the acceleration fields and velocity fields is determined. In this study, we focus on studying the flows of inextensible space-like curves with a space-like principal normal vector specified by a normal acceleration that equals the curvature of the curve. Through the motion of the inextensible space-like curve with normal acceleration, we prove that the position vector of the curve satisfies a one-dimensional wave equation. We present some novel applications and visualize the flows of curves and their curvatures.