Dual Covariant Derivative on Time Scales

The covariant derivative is a kind of derivative along tangent vectors of a curve or surface. The covariant derivative has many applications in physics, kinematics, robotics, machine engineering, and other scientific areas. Additionally, a dual vector or screw-vector in the dual space is an important tool widely used in kinematic and robotic studies to represent the space motion including the rotation and translation transformations. The aim of this paper, to introduce the dual covariant derivative on time scales defined as an arbitrary nonempty closed subset of the real numbers and achieves to unify discrete and continuous forms. Consequently, some properties are analyzed.

Keywords:

Time Scales, Dual Space Dual Covariant Derivative.,

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Aktan, N.,. Sarikaya, M., Ilarslan, K., Yildirim, H., Directional Nabla-derivative and Curves on n-dimensional Time Scales, Acta Applicandae Mathematicae,105(2009), 45--63.
Aulbach, B., Hilger, S., Linear Dynamic Processes with in Homogeneous Time Scale, Nonlinear Dynamics and Quantum Dynamical System, Berlin Academia, Verlag, (1990).
Bohner, M., Peterson, A., Dynamic Equations on timescales}, An Introduction with Applications,Birkhauser,(2001).
Bohner M., Guseinov G., An Introduction to Complex Functions on Products of Two Time Scales, Journal of Difference Equations and Applications,12(2006),369--384.
Dimentberg, F.M., The Screw Calculus and its Applications in Mechanics,Foreign Technology Division, (1965).
Hacısalihoğlu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi Yayınları, Ankara, (1983).
Hilger, S., Analysis on Measure Chains-a Unified Approach to Continuous and Discrete Calculus, Results Mathematics, 18(1990),18--56.
Kramer, E.E.,Functions of the Dual Variable, American Journal of Mathematics, 52(2)(1930), 370--376.
Kusak H.and Çaliskan A., The Delta Nature Connection on Time Scale, Journal of Mathematical Analysis and Applications, 375(1)(2011), 323--330.
Kusak H.and Çaliskan A., Dual-Variable Functions on Time Scale, Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8(3)(2018), 265--278.
Minguzzi, E.A., Geometrical Introduction to Screw Theory, European Journal of Physics, 34(3)(2013).
Messelmi, F., Analysis of Dual Functions, Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, Mechanisms and Machine Theory,4(2013), 37--54.
Study, E., Geometrie der Dynamen, Teubner, Leipzig, (1901).
Taleshian, A., Application of Covariant Derivative in the Dual Space, International Journal of Contemporary Mathematical Sciences,4(17)(2009), 821--826.
Veldkamp, G.R., On the Use of Dual Numbers, Vectors and Matrices in Instantaneous Spatial Kinematics, Mechanism and Machine Theory, 11(1976), 141--156.
Yaglom, I.M., A Simple Non- Euclidean Geometry and Its Physical Basis. An elementary account of Galilean geometry and the Galilean principle of relativity, Springer, (2012).

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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