Dual Covariant Derivative on Time Scales

Abstract

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.