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

Abstract

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.

Keywords

• flows of curves
• evolution of curves
• motion of space-like curves
• motion of time-like curves
• motion by acceleration field
• time evolution equations
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