• Title/Summary/Keyword: representations of angle

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Angle concepts and introduction methods of angles in elementary mathematics textbooks (초등학교 수학 교과서에 제시된 각의 개념과 도입 방법 분석)

  • Kim, Sangmee
    • Education of Primary School Mathematics
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    • v.21 no.2
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    • pp.209-221
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    • 2018
  • Angle concepts have a multifaceted nature such as quantitative aspects as the amount of rotation, qualitative aspects as geometric shapes, and relationship aspects made with planes or lines. This study analysed angle concepts and introduction methods of angles in elementary mathematics textbooks which have been used from the Syllabus Period to the 2015 Revised Mathematics Curriculum. First, the concepts of angles in mathematics textbooks focus through the definitions, representations, and components of angles presented in mathematics textbooks are analyzed. Secondly, how various aspects of each angle are sequenced through the tasks or activties in the introduction of lesson is looked. As a result of analysis, the methods of introducing angles in the changes of mathematics textbooks have mainly focused on learning about geometric shapes and relations of components. In the mathematics classroom, students should experience various aspects of geometric shapes, rotations, relational aspects of points, lines and surfaces, and support and link them to form a wide range of concepts.

ON ANALYTICAL SOLUTION OF NON LINEAR ROLL EQUATION OF SHIPS

  • Tata S. Rao;Shoji Kuniaki;Mita Shigeo;Minami Kiyokazu
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
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    • 2006.10a
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    • pp.134-143
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    • 2006
  • Out of all types of motions the critical motions leading to capsize is roll. The dynamic amplification in case of roll motion may be large for ships as roll natural frequency generally falls within the frequency range of wave energy spectrum typical used for estimation of motion spectrum. Roll motion is highly non-linear in nature. Den are various representations of non-linear damping and restoring available in literature. In this paper an uncoupled non-linear roll equations with three representation of damping and cubic restoring term is solved using a perturbation technique. Damping moment representations are linear plus quadratic velocity damping, angle dependant damping and linear plus cubic velocity dependant damping. Numerical value of linear damping coefficient is almost same for all types but non-linear damping is different. Linear and non-linear damping coefficients are obtained form free roll decay tests. External rolling moment is assumed as deterministic with sinusoidal form. Maximum roll amplitude of non-linear roll equation with various representations of damping is calculated using analytical procedure and compared with experimental results, which are obtained form forced tests in regular waves by varying frequency with three wave heights. Experiments indicate influence of non-linearity at resonance frequency. Both experiment and analytical results indicates increase in maximum roll amplitude with wave slope at resonance. Analytical results are compared with experiment results which indicate maximum roll amplitude analytically obtained with angle dependent and cubic velocity damping are equal and difference from experiments with these damping are less compared to non-linear equation with quadratic velocity damping.

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Design of Aim Angle Following Guidance Law Using Lyapunov Theory (르야프노프 이론을 이용한 목표각 추종 유도법칙 설계)

  • Kim, Ki-Seok;Kim, You-Dan
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.30 no.7
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    • pp.81-89
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    • 2002
  • Guidance laws can be conceptually classified into three categories although their mathematical representations are various and different. In this paper, a generalized conceptual guidance law including the concepts of the above categories is proposed. The aim angle is introduced using the geometry of the collision triangle. The aim angle represents the arbitrary angle between the pursuit angle and the expected collision angle. The objective of the proposed guidance law is to make the aim angle zero asymptotically. It can be shown that the aim angle error response for the considered system is same as that of the first order system. When the autopilot of the missile system has slow dynamics, autopilot time lag may deteriorate the performance of the guidance law performance. In this case, another new guidance law compensating the autopilot time lag effect is proposed. To verify the proposed guidance laws, several numerical simulations are performed.

Attitude control in spacecraft orbit-raising using a reduced quaternion model

  • Yang, Yaguang
    • Advances in aircraft and spacecraft science
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    • v.1 no.4
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    • pp.427-441
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    • 2014
  • Orbit-raising is an important step to place spacecraft from parking orbits into working orbits. Attitude control system design is crucial in the success of orbit-raising. Several text books have discussed this design and focused mainly on the traditional methods based on single-input single-output (SISO) transfer function models. These models are not good representations for many orbit-raising control systems which have multiple thrusters and each thruster has impact on the attitude defined by all outputs. Only one published article is known to use a more suitable multi-input multi-output (MIMO) Euler angle model in spacecraft orbit-raising attitude control system design. In this paper, a quaternion based MIMO model for the orbit-raising attitude control system design is proposed. The advantages of using quaternion based model for orbit-raising control system designs are (a) there is no need for mathematical transformations because the attitude measurements are normally given by quaternion, (b) quaternion based model does not depend on rotational sequences, which reduces the chance of human errors, and (c) the singular point of reduced quaternion model is the farthest from the operational point where linearization is performed. We will show that performance of quaternion model based design will be as good as the performance of Euler angle model based design for orbit-raising problem.

Hydrodynamic characteristics of cambered NACA0012 for flexible-wing application of a flapping-type tidal stream energy harvesting system

  • Sitorus, Patar Ebenezer;Park, JineSoon;Ko, Jin Hwan
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.11 no.1
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    • pp.225-232
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    • 2019
  • In recent years, nonlinear dynamic models have been developed for flapping-type energy harvesting systems with a rigid wing, but not for those with a flexible wing. Thus, in this study, flexible wing designs of NACA0012 section are proposed and measurements of the forces of rigid cambered wings, which are used to estimate the performance of the designed wings, are conducted. Polar curves from the measured lift and drag coefficients show that JavaFoil estimation is much closer to the measured values than Eppler over the entire given range of angles of attack. As the camber of the rigid cambered wings is increased, both the lift and drag coefficients increase, in turn increasing the resultant forces. Moreover, the maximum resultant forces for all rigid cambered wings are achieved at the same angle of attack as the maximum lift coefficient, meaning that the lift coefficient is dominant in representations of the wing characteristics.

Enhanced Representation for Object Tracking (물체 추적을 위한 강화된 부분공간 표현)

  • Yun, Frank;Yoo, Haan-Ju;Choi, Jin-Young
    • Proceedings of the IEEK Conference
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    • 2009.05a
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    • pp.408-410
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    • 2009
  • We present an efficient and robust measurement model for visual tracking. This approach builds on and extends work on subspace representations of measurement model. Subspace-based tracking algorithms have been introduced to visual tracking literature for a decade and show considerable tracking performance due to its robustness in matching. However the measures used in their measurement models are often restricted to few approaches. We propose a novel measure of object matching using Angle In Feature Space, which aims to improve the discriminability of matching in subspace. Therefore, our tracking algorithm can distinguish target from similar background clutters which often cause erroneous drift by conventional Distance From Feature Space measure. Experiments demonstrate the effectiveness of the proposed tracking algorithm under severe cluttered background.

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A study on the Byzantine Costume -An analysis of constructional elements of the Costume Form- (Byzantine시대의 복식에 관한 연구 -복장 형태구성의 요인 해석-)

  • Kim Ok Jin
    • Journal of the Korean Society of Clothing and Textiles
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    • v.3 no.1
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    • pp.25-30
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    • 1979
  • Le propos de la presente consideration est de deceler Ie probleme du costume au niveau de probleme de l'art pur qui, comme dit Hegel, repond a un besoin primitif qui consiste a exterioriser et a concretiser les representations et les idees nees dans I'esprit humain. II va de soi que c'est une sorte de problemes appartenants a la theorie generale du costume. Mais il nous semble que chez nous on a neglige d'analyser les elements du costume sous l'angle de cette exteriorisation de l'idee esthetique que nous avons essay de souligner. Nous avons pris cette fois, pour un modele de ce sujet, les costumes sous Justinien (527-565) de l'Empire byzantin.

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Using CNN- VGG 16 to detect the tennis motion tracking by information entropy and unascertained measurement theory

  • Zhong, Yongfeng;Liang, Xiaojun
    • Advances in nano research
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    • v.12 no.2
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    • pp.223-239
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    • 2022
  • Object detection has always been to pursue objects with particular properties or representations and to predict details on objects including the positions, sizes and angle of rotation in the current picture. This was a very important subject of computer vision science. While vision-based object tracking strategies for the analysis of competitive videos have been developed, it is still difficult to accurately identify and position a speedy small ball. In this study, deep learning (DP) network was developed to face these obstacles in the study of tennis motion tracking from a complex perspective to understand the performance of athletes. This research has used CNN-VGG 16 to tracking the tennis ball from broadcasting videos while their images are distorted, thin and often invisible not only to identify the image of the ball from a single frame, but also to learn patterns from consecutive frames, then VGG 16 takes images with 640 to 360 sizes to locate the ball and obtain high accuracy in public videos. VGG 16 tests 99.6%, 96.63%, and 99.5%, respectively, of accuracy. In order to avoid overfitting, 9 additional videos and a subset of the previous dataset are partly labelled for the 10-fold cross-validation. The results show that CNN-VGG 16 outperforms the standard approach by a wide margin and provides excellent ball tracking performance.

JProtein : A Protein Structure Viewer based on Java3D Technology (JProtein : Java3D 기법을 이용한 단백질 구조 뷰어)

  • Moon Nam-Doo;Byun Sang-Hee;Kim Jin-Hong;Han In-Seob;Lee Myung-Joon
    • The KIPS Transactions:PartD
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    • v.11D no.7 s.96
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    • pp.1517-1526
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    • 2004
  • Entering the post genome era with an increasing amount of protein data available in public databases, the study of tertiary structure of pro-teins has been artively in progress. To analyze the structure of a protein effectively, it is necessary to visualize the tertiary structure of a protein. Rececntly, many visualization tools based on Java technology have been developed to visualize a protein whose structure has been known. In this paper, we describe a new protein visualization system, named JProtein. It is designed to be an easy-to-use, platform neutral melocular visualization tool. The JProtein system is developed using Java3D technology. Java3D is an API providing a programming interface for 3D representations. The system informs us the angle and the distance of the interacting atoms in amino acids which are visualized, providing several 3D representation models of a protein molecule. In particular, the JProtein system presents synchronous stereo view as well as asynchronous one.