The Unsteady laminar flow of an electrically conducting dusty viscous incompressible fluid near an accelerated flat, nonconducting plate, under the influence of a uniform magnetic field and pulsatile pressure gradient has been studied using differential geometry techniques i.e., in Frenet frame field system. The particular cases as (i) impulsively moving and (ii) uniformly accelerated motion of...

A polyhelix is continuous space curve with continuous Frenet frame that consists of a sequence of connected helical segments. The main result of this paper is that given n points in space, there exist infinitely many polyhelices passing through these points. These curves are by construction continuous with continuous derivatives and are completely specified by 3n numbers, i.e., the initial posi...

Frenet frames are a central construction in modern differential geometry, in which structure is described with respect to an object of interest rather than with respect to external coordinate systems. The Cartan moving frame model specifies how these frames adapt when they are transported along the object. We consider this as a model for integrating local information with information in a neigh...

Formulation of governing equations for an elastic cable have a long and dated history. A unified framework to detect the dynamics such systems is detailed, justified, assessed numerically. Modal analyses are performed in Frenet basis, which describes motion local frame accounts accurately system’s physics. In this article, methodology produce arbitrary reduced-order models nonlinear provided. T...

The paper introduces a new kind of special ruled surface. base each surface is taken to be one the Smarandache curves given curve according Frenet frame, and generator (ruling) chosen corresponding unit Darboux vector. characteristics these newly defined surfaces are investigated by means first second fundamental forms their curvatures. An example provided considering both helix Viviani’s curve.

In this paper, position vector of a spacelike general helix with respect to standard frame in Minkowski space E 1 are studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike general helix. In terms of solution, we determine the parametric representation of the general helices from the intrin...

This paper proposes an approach to design the surface pencil with specified parametric representations from a given geodesic. The surface was considered as a combination of the marching-scale functions and the Frenet trihedron frame, for which some necessary and sufficient conditions must be met. This paper simplifies those conditions, and represents the surface by combination of control points...

Solutions are presented for the problem of the motion of a dusty gas through Porous Media in an Open Rectangular Channel. It is assumed that the fluid and the dust particle clouds are static at the beginning. The flow is due to the influence of time dependent pressure gradient. Flow analysis is carried out in Frenet frame field system and exact solutions of the problem are obtained by solving t...