• Proceedings of the KIEE Conference
• /
• 2005.10b
• /
• pp.632-634
• /
• 2005

In this paper, The Frenet-Serret formula of classical geometric curve theory with the concept of a missile pointing velocity vector are used to analyze and design a missile guidance law. The capture capability of this guidance law is qualitatively studied by comparing the rotations of the velocity vectors of missile and target relative to the line of sight vector. when fuzzy Table look-up theory applied in target-missile distance & angle displacement, this research. It's performance is better then classical research.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.1339-1351
• /
• 2015

In this paper, using pseudo-spherical Frenet frame of pseudo-spherical curves in hyperbolic space, we define the notion of the structure functions on the non-developable ruled surfaces with timelike ruling. Then we obtain the properties of the structure functions and a complete classification of the non-developable ruled surfaces with timelike ruling in Minkowski 3-space by the theories of the structure functions.

• The Pure and Applied Mathematics
• /
• v.12 no.4 s.30
• /
• pp.275-287
• /
• 2005

Geometric invariants are basic tools for geometric processing and computer vision. In this paper, we give a linear approximation for the differentiation of the binormal vector field of a space curve by using the forward and backward differences of discrete binormal vectors. Two kind of discrete torsion, say, back-ward torsion $T_b$ and forward torsion $T_f$ can be defined by the dot product of the (backward and forward) discrete differentiation of binormal vectors that are linear approximations of torsion. Using Frenet formula and Taylor series expansion, we give error estimations for the discrete torsions. We also give numerical tests for a curve. Notably the average of $T_b$ and $T_f$ looks more stable in errors.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.963-975
• /
• 2015

In this paper, we give a representation formula for an isotropic curve with pseudo arc length parameter and define the structure function of such curves. Using the representation formula and the Frenet formula, the isotropic Bertrand curve and k-type isotropic helices are characterized in the 3-dimensional complex space $\mathbb{C}^3$.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.4
• /
• pp.525-535
• /
• 2015

In this paper, we study on spinors with two hyperbolic components. Firstly, we express the hyperbolic spinor representation of a spacelike curve dened on an oriented (spacelike or time-like) surface in Minkowski space ${\mathbb{R}}^3_1$. Then, we obtain the relation between the hyperbolic spinor representation of the Frenet frame of the spacelike curve on oriented surface and Darboux frame of the surface on the same points. Finally, we give one example about these hyperbolic spinors.

• Proceedings of the KSME Conference
• /
• 2001.06b
• /
• pp.355-360
• /
• 2001

By using Frenet formulation and Timoshenko beam theory, the partial differential equations of motion are derived for a helical spring having a doubly symmetrical cross section subjected to the pre-load axially. These equations of motion are solved to give the dispersion relationship and dynamic stiffness matrix is assembled. Natural frequencies are obtained from the receptance of the system. The results of the dynamic stiffness method are compared with those of the transfer matrix method from published examples and finite element method.

• Honam Mathematical Journal
• /
• v.45 no.4
• /
• pp.668-677
• /
• 2023

In this study, we bring forth a new general formula for inextensible flows of Euclidean curves as regards modified orthogonal frame (MOF) in E³. For an inextensible curve flow, we provide the necessary and sufficient conditions, which are denoted by a partial differential equality containing the curvatures and torsion.