• 호남수학학술지
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• 제42권1호
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• pp.187-195
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• 2020

In this paper, we investigate the vectorial moments of Bäcklund transformations of a space curve in 𝔼³. Firstly, it is obtained the vectorial moments which named α𝓖 dual curve, β𝓖 dual curve, and γ𝓖 dual curve of Bäcklund transformations. Then we give the Euler elastic bending energies of these curves. Finally, we provide some examples of α𝓖 dual, β𝓖 dual, and γ𝓖 dual, and their Euler elastic bending energies.

• Journal of Mechanical Science and Technology
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• 제20권3호
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• pp.376-381
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• 2006

In this paper, the quaternion, the dual Euler, and the direction cosine methods are numerically compared using a non-aerodynamic 6 degree-of-freedom rigid model at all-attitude angles of an aircraft. The dual Euler method turns out to be superior to the others in the applications because it shows better numerical accuracy, stability, and robustness in integration step sizes. The dual Euler method is affordably less efficient than the quaternion method in terms of computational cost. Numerical accuracy and stability, which allow larger integration step sizes, are more critical in modern real-time applications than computational efficiency because of today's increased computational power. If the quaternion method is required because of constraints in computation time, then a suppression mechanism should be provided for algebraic constraint errors which will eventually add computational burden.

• 한국수학교육학회지시리즈A:수학교육
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• 제16권2호
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• pp.29-31
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• 1978

bipartite graph와 Euler graph의 정의를 사용하는 대신 이들 graph가 나타내는 특성을 사용하여 bipartite matroid와 Euler matroid를 정의하고 이들 matroid가 binary일 때 서로 dual 의 관계가 있음을 증명한다. 이 관계를 이용하여 bipartite graph와 Euler graph의 성질을 밝힐수 있다.

• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.493-506
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• 2009

By using the improved Euler-Maclaurin summation formula and estimating the weight coefficients in this paper, a new dual Hardy-Hilbert's inequality and its reverse form are obtained, which are all with two pairs of conjugate exponents (p, q); (r, s) and a independent parameter ${\lambda}$. In addition, some equivalent forms of the inequalities are considered. We also prove that the constant factors in the new inequalities are all the best possible. As a particular case of our results, we obtain the reverse form of a famous Hardy-Hilbert's inequality.

• Structural Engineering and Mechanics
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• 제64권2호
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• pp.205-212
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• 2017

Based on the coupled elastic bending deformation features and relationships between the internal force and deformation of pre-twisted Euler beam, the generalized strain, the equivalent constitutive equation and the equilibrium equation of pre-twisted Euler beam are developed. Based on the properties of the dual-antisymmetric matrix, the general solution of pre-twisted Euler beam is obtained. By comparison with ANSYS solution by using straight Beam-188 element based on infinite approach strategy, the results show that the developed method is available for pre-twisted Euler beam and also provide an accuracy displacement interpolation function for the subsequent finite element analysis. The effect of pre-twisted angle on the mechanical property has been investigated.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2001년도 춘계 학술대회논문집
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• pp.78-84
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• 2001

A dual-time stepping algorithm combined with a parallelized multigrid DADI method is presented to predict the dynamic damping coefficients. The Basic Finner model is chosen to validate the prediction capability of the present unsteady Euler method. The linearity of the pitch- and roll-damping coefficients is shown in the low angular rates and the interesting large drop and stiff increment in transonic region for roll-damping coefficients are explained in detail. Through the analysis for the pressure distributions at Mach number 1.0 to 1.2, the sudden drop results from the normal shock and the stiff increment of roll-damping reflects the transition of the normal shock to the oblique shock. The results also show that the Euler equations can give the damping coefficients with a comparable accuracy.

• 한국항공우주학회지
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• 제33권10호
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• pp.10-16
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• 2005

본 연구에서는 3차원 시간 정확도를 가진 오일러 공탄성 해석 기법을 개발하였다. 유체-구조를 연계 시 발생할 수 있는 지연(lagging) 오차를 감소시키기 위해서 2차의 staggered 알고리즘을 적용하였다. 비정상 공력 해석과정에서 시간 정확도와 계산 시간을 줄이기 위해 사용된 병렬화된 다중격자기법(parallelized multi-grid method)과 DADI 기법을 기반으로 된 이중시간전진기법(dual-time stepping method)을 사용하였다. 오일러 공탄성 코드의 검증을 위해서 AGARD 445.6 날개 모델의 공탄성 해석을 수행하였다. 해석 결과는 실험값 및 다른 참고문헌의 해석 결과와 비교하였으며, 본 연구의 해석 결과가 다른 참고 문헌의 해석 결과들과 비교하여 상대적으로 실험값에 근접하였다.

• 한국전기전자재료학회논문지
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• 제15권10호
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• pp.914-920
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• 2002

This study investigates the mechanism of a dual mode probe that generates both of the longitudinal and shear waves simultaneously with a single FZT element. Most of conventional ultrasonic probes are constructed to generate either longitudinal or shear waves. After poling, PZT has the hexagonal 6mm crystal symmetry. All possible crystal cuts are checked to determine appropriate Euler transformation angles for efficient excitation of dual modes. For the selected cut, performance of the dual mode element is analyzed through numerical simulation and experiments. Results of the analysis determine the optimal crystal cut for simultaneous generation of P and S waves of equal strength.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2000년도 추계학술대회 논문집
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• pp.670-673
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• 2000

This paper attempt analysis and computer simulation of dynamics of a set of dual multi-joint fingers with soft-deformable tips which are grasping. Firstly, a set of differential equation describing dynamics of the fingers and object together with geometric constraint of tight area-contacts is formulated by Euler-Lagrange's formalism. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Finally, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• Journal of Mechanical Science and Technology
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• 제20권11호
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• pp.1961-1971
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• 2006

A soft recovery system (SRS) is a device that stops a high speed projectile without damaging the projectile. The SRS is necessary to verify the shock resistant requirements of microelectronics and electro-optic sensors in smart munitions, where the projectiles experience over 20,000 g acceleration inside the barrel. In this study, a computer code for the performance evaluation of a SRS based on ballistic compression decelerator concept has been developed. It consists of a time accurate compressible one-dimensional Euler code with use of deforming grid and a projectile motion analysis code. The Euler code employs Roe's approximate Riemann solver with a total variation diminishing (TVD) method. A fully implicit dual time stepping method is used to advance the solution in time. In addition, the geometric conservation law (GCL) is applied to predict the solutions accurately on the deforming mesh. The equation of motion for the projectile is solved with the four-stage Runge-Kutta time integration method. A small scale SRS to catch a 20 mm bullet fired at 500 m/s within 1,600 g-limit has been designed with the proposed method.