Normal Fermi- Walker Derivative
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.
___
- [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.
- ISSN: 2147-6268
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2013
- Yayıncı: -