• Title/Summary/Keyword: Mathematica simulation

검색결과 13건 처리시간 0.022초

복합 나노미터 패턴 도광판의 광특성 (Optical Characteristics of the LGP with Nanometer-patterned Sizes on Its Both Surfaces)

  • 홍진수;김창교;이병욱;김경래
    • 제어로봇시스템학회논문지
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    • 제14권6호
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    • pp.530-534
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    • 2008
  • The LGP with nanometer structures resulted in enhancement of optical efficiency. Its fundamental mechanism is to recycle the polarized light via one round-trip through QWP(Quarter-wave Plate) but the maximum efficiency to reach with this method is limited up to 2. To get the larger efficiency than this a LGP with 1D PC(one-dimensional photonic crystal) nanometer-patterned on its top and bottom surfaces is suggested. For its optimum design the computer simulation is performed and suggests a grating that the spatial frequency between adjacent patterns is 500nm, its height 250nm, duty cycle 50%, and its cross section is rectangular. The angles of transmitted light are nearly the same as the results expected from the generalized Snell's law. Thus the Mathematica code, developed in this experiment, will be applied to designing the optimized LGP. The LGP with nanometer-patterened 1D PC LGP on its both surfaces shows the enhancement of transmitted intensity distribution up to 5.7 times.

라그랑지 방법을 이용할 철봉 몸굽혀 휘돌기 동작의 시뮬레이션 (Simulation of Scooped Swing in High Bar Using Lagrange's Method : A Case Study)

  • 하종규
    • 한국콘텐츠학회논문지
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    • 제7권4호
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    • pp.234-240
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    • 2007
  • 이 연구는 철봉 몸굽혀 휘돌기 동작의 최적 모델을 구축하는 것이다. 연구 대상자는 국가대표 남자체조선수(나이 18세, 신장 153cm, 질량 48kg) 1명을 선정하였고, K대학교 체조장에 기 설치된 Spieth사의 철봉을 이용하여 실험하였다. 먼저 대상자에게 연구의 목적과 주의 사항을 주지시키고 사전 서면동의를 받은 후 실험을 실시하였다. 인체를 2분절로 모형화한 몸 굽혀 휘돌기 동작의 영상분석을 위하여 Qualisys사의 카메라(MCU-240) 6대와 소프트웨어인 QTM(Qualisys Track Mannager)을 사용하였다. 이 동작을 이중진자(HAT/total leg)로 모형화하고 라그랑지 운동방정식의 파라메터에 실험에서 획득한 수치를 입력하여 시뮬레이션하였다. 데이터 처리와 모델(미분 연립 방정식)의 해는 Mathematicas5.0으로 프로그래밍하여 구하였다. 분석변인에 대한 모델치와 실험치의 비교 결과는 첫째, 철봉의 최대변위는 모델치(약 0.18 m)가 실험치(약 0.16 m)보다 약 0.02m 더 크게 나타났다. 둘째, 분절1(HAT)의 각변위 패턴은 모두 증가곡선을 보였으나 변곡점의 차이가 나타났다. 셋째, 분절2(total leg)의 각변위 패턴은 전반적으로 유사하게 나타났으나 최대 각은 약 $4^{\circ}$ 차이를 보였다. 결론적으로 실험치와 일치하는 최적모델을 도출하지는 못하였지만 라그랑지 모델을 통한 시뮬레이션의 가능성을 제시하였다. 향후 제한된 2분절 모형을 3, 4분절 모델로 확장하고 생체물성(근골격계)을 정확하게 표현하는 물리적 도구를 개발하는 연구와 인체시스템을 근골격계와 근신경계을 통합한 모델구축이 이루어져야 하겠다.

복합진자 모형의 뉴튼.오일러 알고리즘 비교 (Comparison of Newton's and Euler's Algorithm in a Compound Pendulum)

  • 하종규
    • 한국운동역학회지
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    • 제16권3호
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    • pp.1-7
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    • 2006
  • The Primary type of swinging motion in human movement is that which is characteristic of a pendulum. The two types of pendulums are identified as simple and compound. A simple pendulum consist of a small body suspended by a relatively long cord. Its total mass is contained within the bob. The cord is not considered to have mass. A compound pendulum, on the other hand, is any pendulum such as the human body swinging by hands from a horizontal bar. Therefore a compound pendulum depicts important motions that are harmonic, periodic, and oscillatory. In this paper one discusses and compares two algorithms of Newton's method(F = m a) and Euler's method (M = $I{\times}{\alpha}$) in compound pendulum. Through exercise model such as human body with weight(m = 50 kg), body length(L = 1.5m), and center of gravity ($L_c$ = 0.4119L) from proximal end swinging by hands from a horizontal bar, one finds kinematic variables(angle displacement / velocity / acceleration), and simulates kinematic variables by changing body lengths and body mass. BSP by Clauser et al.(1969) & Chandler et al.(1975) is used to find moment of inertia of the compound pendulum. The radius of gyration about center of gravity (CoG) is $k_c\;=\;K_c{\times}L$ (단, k= radius of gyration, K= radius of gyration /segment length), and then moment of inertia about center of gravity(CoG) becomes $I_c\;=\;m\;k_c^2$. Finally, moment of inertia about Z-axis by parallel theorem becomes $I_o\;=\;I_c\;+\;m\;k^2$. The two-order ordinary differential equations of models are solved by ND function of numeric analysis method in Mathematica5.1. The results are as follows; First, The complexity of Newton's method is much more complex than that of Euler's method Second, one could be find kinematic variables according to changing body lengths(L = 1.3 / 1.7 m) and periods are increased by body length increment(L = 1.3 / 1.5 / 1.7 m). Third, one could be find that periods are not changing by means of changing mass(m = 50 / 55 / 60 kg). Conclusively, one is intended to meditate the possibility of applying a compound pendulum to sports(balling, golf, gymnastics and so on) necessary swinging motions. Further improvements to the study could be to apply Euler's method to real motions and one would be able to develop the simulator.