Normal Fermi- Walker Derivative

Yıl 2017, Cilt: 5 Sayı: 1, 1 - 8, 30.04.2017

Özgür Keskin Yusuf Yaylı

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

Cited By: 2

Öz

 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.

Anahtar Kelimeler

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

Kaynakça

• [1] Balakrishnan R., Space curves, anholonomy and nonlinearity. Prama J. Phys. 64 (2005), no. 4, 607-615.
• [2] Benn I.M. and Tucker R.W., Wave mechanics and inertial guidance. Phys. Rev. D. 39 (1989), no. 6, 1594-1601.
• [3] Berry M.V., Proc. Roy. Soc. London A. (1984), 392.
• [4] Calin C. and Crasmareanu M., Slant Curves and Particles in three- dimensional Warped Products and their Lancret invariants. Bulletin of the Australian Mathematical Society. 88 (2013), no. 1, 128-142.
• [5] Crasmareanu M. and Frigioiu C., Unitary vector fields are Fermi-Walker transported along Rytov-Legendre curves. Int. Journal of Geometric Methods in Modern Physics. 12 (2015), 1550111.
• [6] Dandolof R., Berry’s phase and Fermi-Walker parallel transport. Phys. Lett. A. 139 (1989), no. (1,2), 19-20. [7] Fermi E. Atti Accad. Naz., Lincei Cl. Sci. Fiz. Mat. Nat. 31 (1922), 184-306.
• [8] Hawking S.W. and Ellis G.F.R., The Large Scale Structure of Spacetime. Cambridge University Press., 1973.
• [9] Karakus F. and Yayli Y., On the Fermi-Walker derivative and non-rotating frame. Int. Journal of Geometric Methods in Modern Physics. 2012, no. (9,8), 1250066.
• [10] Karakus F. and Yayli Y., The Fermi- Walker derivative in Lie groups. Int. Journal of Geometric Methods in Modern Physics. 10 (2013), no. 7, Article ID 1320011:10p.
• [11] Karakus F. and Yayli Y., The Fermi derivative in the hypersurfaces. Int. Journal of Geometric Methods in Modern Physics. 12 (2015), no. 1, Article ID 1550002:12p.
• [12] Scofield P.D., Curves of Constant Precession. The American Mathematical Monthly 102 (1995), no. 6, 531-537.
• [13] Uzunoglu B., Gok I. and Yayli Y., A new approach on curves of constant precession. Applied Mathematics and Computation. 275 (2016), 317–323.