The Fermi–Walker Derivative in Minkowski Space $${E_{1}^{3}}$$ E 1 3

Abstract

In this study Fermi–Walker derivative, Fermi–Walker parallelism, non-rotating frame, Fermi–Walker terms Darboux vector concepts are given for Minkowski 3-space \({E_{1}^{3}}\). First, we get any spacelike curve with a spacelike or timelike principal normal and any vector field along the curve in Minkowski 3-space \({E_{1}^{3}}\). Fermi–Walker derivative and Fermi–Walker parallelism are analyzed for any spacelike curve with a spacelike or timelike principal normal in Minkowski 3-space \({E_{1}^{3}}\) and the necessary conditions to be Fermi–Walker parallel are explained. Then the necessary definitions, concepts and theorems are analyzed about Fermi–Walker derivative for any spacelike curve with a lightlike(null) principal normal. And then, in Minkowski 3-space \({E_{1}^{3}}\) Fermi–Walker derivative is analyzed for any timelike curves.