• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.9
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• pp.875-881
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• 2010

During the lunar mission, spacecraft are subject to various unexpected disturbance sources such as third body attraction, solar pressure and operating impulsive maneuver error. Therefore, efficient trajectory correction maneuver (TCM) strategy must be required to follow the designed mission trajectory. In the early days of space exploration, the mission trajectory has been designed by using patched conic approach based on two-body dynamics for the lunar mission. Thus the TCM based on two-body dynamics has been usually adopted. However, with the advanced in computing power, the mission trajectory based on three-body dynamics is attempted recently. Thus, these approaches based on two-body dynamics are essentially different from real environment and large amount of energy for the TCM is required. In this work, we study the trajectory correction maneuver based on three-body dynamics.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.5
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• pp.46-55
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• 2006

In general, 3-dimensional point-mass equation has been widely used for the trajectory optimization of the fixed-wing aircraft and reentry vehicle. But it should be modified and represent target vehicle's own characteristics. For a lighter-than-air vehicle such as an airship, there exists different and peculiar flight characteristics compared with the aircraft. The first part of this paper is to derive the dynamic equation of motion for the mid-altitude unmanned airship and the second part is to obtain the optimal trajectories under the minimal time flight given constraints. The trajectory optimization problem is converted into the nonlinear programming problem using Sequential Quadratic Programming approach. Finally numerical solutions are presented in the last part of the paper.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.3
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• pp.213-220
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• 2014

A program that predicts trajectories of projectiles influenced by the interference flow field of helicopters is developed. The interference flow field are computed using a compressible inviscid solver in conjunction with an actuator disc model. The trajectories are predicted using 6-DOF (Degree of Freedom) equations as well as an alternative form of modified point mass equations of motion. The method for the interference flow field prediction method are validated with ROBIN(ROtor Body INteraction) model. A Sierra international bullet and a 105mm projectile are used to validate the trajectory method. Trajectories of a Sierra International bullet and a HYDRA 70 rocket firing from a helicopter are predicted.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.683-690
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• 1985

본 논문에는 Euler매개변수를 회전좌표계로 사용하여 구속된 3차원 기계시스템의 역동학력 해 을 수행한 연구결과가 수록되었다. 해석을 위해 문제에 등장하는 비선형 Holonomic구속조건식 들과 운동방정식들을 Cartesian일반좌표계을 사용하여 표시하였으며, 일반좌표계를 구성하는 각 강체의 좌표계로는 변위를 나타내기 위한 3개의 좌표와 회전을 나타내기 위한 4개의 Euler매 개변수가 사용되었다. 구속조건식들과 미분방정식 형태의 운동방정식들을 결합하여 시스템 전 체의 운동방정식을 유도하기 위해 Lagrange승수 기법을 사용하였다. 각 강체의 주어진 시간에 서의 위치, 속도, 가속도는 기구학적 해석(kinematic analysis)을 통해 얻어지고, 이 자료들을 전 체운동방정식에 대입하여 Lagrnage승수의 값을 계산하여 6개의 자유도를 가진 로봇 기구를 원 하는대로 운전하는에 필요한 각 관절의 토오크를 계산하였으며, 계산결과가 정확하다는 사실이 입증되었다. 연구결과 Euler매개변수를 회전좌표로 사용할 경우 특이 경우(singular case)가 발 생하지 않으며, 이 방법은 역동력학 해석용 다목적 전산프로그램 개발에 광범위하게 응용될 수 있음이 밝혀졌다.

• Bulletin of the Korean Space Science Society
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• 2011.04a
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• pp.24.3-24.3
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• 2011

우주발사체를 이용하여 인공위성을 궤도에 올리는 문제에서 가장 중요시해야 할 부분은 임무의 성공, 즉 정밀한 궤도 진입이다. 이것이 만족되어졌을 때, 비용의 최소화 또한 설계 시 중요한 고려사항이 된다. 이 두 가지 문제를 동시에 해결하기 위해선 최적 제어 전략이 필요한데, 통상적으로 이 과정은 발사 전에 최적화 기법 등을 이용하여 계산되고 검증된다. 그러나 기존의 최적화 기법은 대부분 선형 시스템에 적합한 기법들 이고, 우주발사체와 같이 매우 복잡하고 강한 비선형을 가진 운동방정식을 최적화 하려면 많은 계산이 소요된다. 계산 소모 시간을 줄이기 위해서는 선형화 등의 기법이 사용되는데, 그러한 경우 최적 해에 대한 신뢰도가 낮아질 수밖에 없다. 이 논문에서는 그러한 문제를 해결하기 위해 최근 활발히 연구되고 있는 비선형 최적화 기법인 상태 의존 Riccati 방정식 기법 (SDRE)을 이용하여 인공위성을 주어진 궤도에 진입시키는 우주발사체의 최적궤도를 계산하였다. 또한 Hamiltonian 을 이용하여 산출된 궤도의 최적성을 보이고, 목표한 궤도와의 비교를 통해 제어기의 정밀성을 확인하였다.

• Journal of Astronomy and Space Sciences
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• v.2 no.1
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• pp.19-33
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• 1985

The singularities of differential Newtonian equation of motion in three body problem cause the loss of accuracy and the considerable increase of the computer time. These singularities could be eliminated during the process of regularization to transform the independent variables and the coordinate of Newtonian equations of motion. In this study, we calculated the positions and velocities of three body along the time scale to find out the unique solution of regularized Newtonian equations of motion with the $5^{th}$ order Runge-Kutta method by assuming the suitable initial velocities and positions. As the results of these calculations it is shown that the tripe stellar system eventually distintegrated, two of them formed a binary, and the last one escaped from this system with a hyperbolic orbit. This may suggest one possible explanation for the binary formation.

• Journal of Korean Society of Steel Construction
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• v.10 no.3 s.36
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• pp.509-523
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• 1998

A consistent finite element formulation and analytic solutions are presented for stability of thin-walled circular arch. The total potential energy is derived by applying the principle of linearized virtual work and including second order terms of finite semitangential rotations. As a result, the energy functional corresponding to the semitangential moment is newly derived. Analytic solutions for the out-of-plane buckling of symmetric thin-walled curved beam subjected to pure bending or uniform compression with simply supported boundary conditions are obtained. For finite element analysis, the cubic Hermitian polynomials are utilized as shape functions and $16{\times}16$ stiffness matrix for curved beam elements and $14{\times}14$ stiffness matrix for straight beam elements are evaluated, respectively. In order to illustrate the accuracy of this study, analytical and numerical results for lateral buckling problems of circular arch are presented and compared with available analytical solutions.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.1
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• pp.41-54
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• 1999

For free vibration of non-symmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for in-plane free vibration behaviors of simply supported thin-walled curved beams with monosymmetric cross-sections is newly derived. Also, a finite element formulation using two noded curved beams element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the straight beam element and the ABAQUS's shell element.

• Nuclear Engineering and Technology
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• v.19 no.3
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• pp.192-197
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• 1987

Two-point kinetic equations for a compact-core-with-bulky-D$_2$O-reflector system were developed. A unique feature of the system is that certain fission gammas create retarded photoneutrons in the D$_2$O reflector by (ｒ, n) reaction. Coupling effect between the core and the reflector was investigated by simulating power transients with various ramp reactivity insertions. Special attention was paid to the phenomenon associated with spatial separation of photoneutrons and their precursors. Simulations show that accuracy of the two-point model is comparable with that of space-dependent approach. Also it is found that the explicily expressed photoneutron terms in the reflector equation slow down the power transient compared to non-photoneutron expressions. Detectors for reactor power control purpose prefer to be deployed in the core zone to be able to accurately perdict transient power.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.2
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• pp.57-68
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• 1998

For free vibration of monosymmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for free vibration behaviors of simply supported thin-walled curved beam element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the FEM using straight beam element.