Normal Fermi- Walker Derivative

Year 2017, Volume: 5 Issue: 1, 1 - 8, 30.04.2017

Özgür Keskin Yusuf Yaylı

https://doi.org/10.36753/mathenot.421468

Cited By: 3

Abstract

 In this paper, first, we defined normal Fermi-Walker derivative and applied for adapted frame. Normal
Fermi-Walker parallelism, normal non-rotating frame and Darboux vector of normal Fermi-Walker
derivative by using normal Fermi-Walker derivative are given for adapted frame. Being conditions of
normal Fermi-Walker derivative and normal non-rotating frame are researched throughout curve for
Frenet frame and Adapted frame. It is shown that vector field which take part in [13] is normal FermiWalker
parallel in accordance with the normal Fermi-Walker derivative along the general helix. Also, we
show that the Frenet frame is normal non-rotating frame in accordance with the normal Fermi-Walker
derivative. Afterwards, we testified that the adapted frame is normal non-rotating frame throughout the
general helix.

Keywords

Frenet frame, Darboux frame, Non-rotating frame, Fermi-Walker derivative

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