• International Journal of Control, Automation, and Systems
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• 제4권4호
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• pp.480-485
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• 2006

In this paper, the error investigation of a 3-dimensional GPS attitude determination system using the error covariance analysis is given. New efficient formulas for computing the Euler Angle Dilution of Precision (EADOP) are also derived. The formulas are easy to compute and represent the attitude error as a function of the nominal attitude of a vehicle, the baseline configuration and the receiver noise. Using the formula, the accuracy of the Euler angle can be analytically predicted without the use of computer simulations. Applications to some configurations reveal the effectiveness of the proposed method.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.573-591
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• 2013

In this paper, we improve the error corrected Euler method(ECEM) introduced in [11] by evaluating function values only at local nodes in each time interval. As a result, one can avoid computations of Jacobian matrices on each time interval so that the algorithms become simpler to implement in solving various class of time dependent differential equations numerically. The proposed ECEM formula resembles to the Runge-Kutta method in its representations but both methods have different characteristic properties.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.329-342
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• 2016

Recently, Korobov polynomials have been received a lot of attention, which are discrete analogs of Bernoulli polynomials. In particular, these polynomials are used to derive some interpolation formulas of many variables and a discrete analog of the Euler summation formula. In this paper, we extend these family of polynomials to consider the Korobov polynomials of the fifth kind and of the sixth kind. We present several explicit formulas and recurrence relations for these polynomials. Also, we establish a connection between our polynomials and several known families of polynomials.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.296-301
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• 2005

This paper describes the kinematics, dynamics and control of a 6-DOF shaking table with a bell crank structure, which converts the direction of reciprocating movements. In this shaking table, the bell crank mechanism is used to reduce the amount of space needed to install the shaking table and create horizontal displacement of the platform. In kinematics, joint design is performed using $Gr{\ddot{u}}bler's$ formula. The inverse kinematics of the shaking table is discussed. The derivation of the Jacobian matrix is presented to evaluate singularity conditions. Considering the maximum stroke of the hydraulic actuator, collision between links and singularity, workspace is computed. In dynamics, computations are based on the Newton-Euler formulation. To derive parallel algorithms, each of the contact forces is decomposed into one acting in the direction of the leg and the other acting in the plane orthogonal to the direction of the leg. Applying the Newton-Euler approach, the solution of inverse dynamics is almost completely parallel. Only one of the steps-the application of the Newton-Euler equations to the platform-must be performed on one single processor. Finally, the efficient control scheme is proposed for the tracking control of the motion platform.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.1-15
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• 2005

In this article, a generalisation of Sard's inequality for Appell polynomials is obtained. Estimates for the remainder are also provided.

• 대한수학회지
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• 제53권2호
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• pp.287-304
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• 2016

In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of ${\mathbb{R}}^n$, $n{\geq}3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is ${\beta}{\in}[1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.

• 호남수학학술지
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• 제35권4호
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• pp.639-645
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• 2013

We aim at presenting certain integral representations for the Riemann Zeta function ${\zeta}(s)$ at positive integer arguments by using some known integral representations of log ${\Gamma}(1+z)$ and ${\psi}(1+z)$.

• 호남수학학술지
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• 제34권3호
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• pp.311-326
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• 2012

The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the definition given recently by the authors [29]. In particular, we obtain a new addition formula for the new class of the generalized Bernoulli polynomials. We also give an extension and some analogues of the Srivastava-Pint$\acute{e}$r addition theorem [28] for both classes. Finally, by making use of the new adition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.

• 대한수학회보
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• 제52권3호
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• pp.741-749
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• 2015

The Changhee polynomials and numbers are introduced in [6]. Some interesting identities and properties of those polynomials are derived from umbral calculus (see [6]). In this paper, we consider Witt-type formula for the n-th twisted Changhee numbers and polynomials and derive some new interesting identities and properties of those polynomials and numbers from the Witt-type formula which are related to special polynomials.

• Nuclear Engineering and Technology
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• 제28권6호
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• pp.583-593
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• 1996

An elastic stiffness formula of a leaf type holddown spring(HDS) assembly with a uniformly tapered width from $w_0$ to $w_14$ over the length, has been analytically derived based on Euler beam theory and Castigliano's theorem. Elastic stiffnesses of the tapered-width leaf type HDSs(TW-HDSs) designed in the same dimensional design spaces as the KOFA HDSs have been evaluated from the derived formula, in addition, a parametric study on the elastic stiffness of the TW-HDSs has been carried out. Analysis results show that, as the effects of axial and shear force on the elastic stiffness of He TW-HDSs have been 0.15~0.21% of the elastic stiffness, most of the elastic stiffness is attributed to the bending moment, and that elastic stiffnesses of the TW-HDSs have been about 32~33% higher than those of the KOFA HDSs. It is found that the number of leaves composing a HDS assembly could be lessened by one under the conditions that the TW-HDSs have been adopted in KOFA.