t. ikawa obtained an ordinary differential equation for the circular helix. recently, the helix havebeen investigated by many differential geometers such as t. ikawa, h. balgetir, m. bektas, m. ergut, n.ekmekci and h. h. hacısalihoglu. in this paper, making use of this author’s methods, we obtainedcharacterizations of helix for a curve with respect to the frenet frame in 3-dimensional galilean ...

The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, geometrical ones, namely curvature torsion. proposed approach is based on Frenet frame utilized in differential geometry provides a general framework for definition of time derivative quantities stationary well transient conditions. As byproduct, unifies generalizes time- phasor-domai...

In this paper we generalize the method of sweeping, which may be used for both object representation and object visualization, to objects in E 4. The generalized sweeping method involves a trajectory in E 4 , and a three-dimensional cross-section orthogonal to the trajectory. Three alternatives are considered for specifying the relationship between the trajectory and the cross-section, namely t...

The Hamiltonian formulation of the dynamics of a relativistic particle described by a higher-derivative action that depends both on the first and the second Frenet-Serret curvatures is considered from a geometrical perspective. We demonstrate how reparametrization covariant dynamical variables and their projections onto the Frenet-Serret frame can be exploited to provide not only a significant ...

Many types of common objects, such as tools and vehicles, usually move in simple ways when they are wielded or driven: the natural axes of the object tend to remain aligned with the local trihedron defined by the object’s trajectory. Based on this observation we use a model called Frenet-Serret motion which corresponds to the motion of a moving trihedron along a space curve. Knowing how the Fre...

Many types of common objects, such as tools and vehicles, usually move in simple ways when they are wielded or driven: The natural axes of the object tend to remain aligned with the local trihedron defined by the object's trajectory. Based on this observation we use a model called Frenet-Serret motion which corresponds to the motion of a moving trihedron along a space curve. Knowing how the Fre...

It is shown that the integrability conditions of the equations satisfied by the local Frenet frame associated with a holomorphic curve in a complex Grassmann manifold coincide with a special class of nonabelian Toda equations. A local moving frame of a holomorphic immersion of a Riemann surface into a complex Grassmann manifold is constructed and the corresponding connection coefficients are ca...

Autonomous vehicles are an essential tool for promoting the development of intelligent transportation systems (ITS) and can effectively reduce traffic accidents caused by human errors. As important part automatic driving software system, path planning is responsible generating motion trajectory vehicle, which primary factor determining quality. However, solution space construction optimization ...

The paper investigates some special Smarandache curves according to Flc-frame in Euclidean 3-space. Frenet and Flc frame vectors, curvature torsion of the new constructed are expressed by means initial curve invariants. For sake comparison view, an example for both is also presented at end paper.

The sweeping surface, or generalized cylinder, is important in graphics, computer vision and elsewhere. A rotation minimizing frame, avoid the unnecessary twist given it by the Frenet frame. We give a quadratically convergent algorithm for computing it along a 3D trajectory curve, with an error bound. This is then used to create NURBS-approximated sweeping surfaces, to aid its incorporation int...