Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space

Abstract

In this study, we first show that the system of Frenet-like differential equation characterizing timelike curves of constant breadth is equivalent to a third order, linear, differential equation with variable coefficients. Then, by using a rational approximation based on Bernstein polynomials, we obtain the set of solution of the mentioned differential equation under the given initial conditions. Furthermore, we discuss that the obtained results are useable to determine timelike curves of constant breadth in Minkowski 3-space E1 3.