• Journal for History of Mathematics
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• v.25 no.4
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• pp.53-67
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• 2012

Today, it is necessary to calculate orbits with high accuracy in space flight. The key words of Poincar$\acute{e}$ in celestial mechanics are periodic solutions, invariant integrals, asymptotic solutions, characteristic exponents and the non existence of new single-valued integrals. Poincar$\acute{e}$ define an invariant integral of the system as the form which maintains a constant value at all time $t$, where the integration is taken over the arc of a curve and $Y_i$ are some functions of $x$, and extend 2 dimension and 3 dimension. Eigenvalues are classified as the form of trajectories, as corresponding to nodes, foci, saddle points and center. In periodic solutions, the stability of periodic solutions is dependent on the properties of their characteristic exponents. Poincar$\acute{e}$ called bifurcation that is the possibility of existence of chaotic orbit in planetary motion. Existence of near exceptional trajectories as Hadamard's accounts, says that there are probabilistic orbits. In this context we study the eigenvalue problem in early 20th century in three body problem by analyzing the works of Darwin, Bruns, Gyld$\acute{e}$n, Sundman, Hill, Lyapunov, Birkhoff, Painlev$\acute{e}$ and Hadamard.

• Journal of Aerospace System Engineering
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• v.15 no.3
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• pp.45-56
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• 2021

Demand for UAM (Urban Air Mobility) aircraft is rapidly increasing in countries around the world due to the problem of traffic congestion in urban areas. Through research and development, various e-VTOL aircraft concepts are being prepared for commercialization, for which airworthiness certification is required, since it is a manned transportation mode for people to board. Factors that pose a fatal threat to the safe operation of UAM aircraft include lightning strikes that can cause damage to structures and disturb the navigation system, as well as icing that impairs flight stability. Since the current UAM aircraft-related lightning and icing certification technology development is insufficient, there is need to develop appropriate airworthiness certification guidelines. In this study, after analyzing the laws and regulations related to aircraft by the FAA and the EASA, we tried to incorporate the lightning and icing certification guidelines for the UAM aircraft. We also analyzed the effects of lightning and icing on UAM aircraft using computational simulation, and presented the basis for establishing practical guidelines for the certification of UAM aircraft to be adopted in the future.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.7
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• pp.445-454
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• 2022

Ice accretion on the aircraft components, such as wings, fuselage, and empennage, can occur when the aircraft encounters a cloud zone with high humidity and low temperature. The prevention of ice accretion is important because it causes a decrease in the aerodynamic performance and flight stability, thus leading to fatal safety problems. In this study, a shape design optimization of a multi-element airfoil is performed to minimize the amount of ice accretion on the high-lift device including leading-edge slat, main element, and trailing-edge flap. The design optimization framework proposed in this paper consists of four major parts: air flow, droplet impingement and ice accretion simulations and gradient-free optimization algorithm. Reynolds-averaged Navier-Stokes (RANS) simulation is used to predict the aerodynamic performance and flow field around the multi-element airfoil at the angle of attack 8°. Droplet impingement and ice accretion simulations are conducted using the multi-physics computational analysis tool. The objective function is to minimize the total mass of ice accretion and the design variables are the deflection angle, gap, and overhang of the flap and slat. Kriging surrogate model is used to construct the response surface, providing rapid approximations of time-consuming function evaluation, and genetic algorithm is employed to find the optimal solution. As a result of optimization, the total mass of ice accretion on the optimized multielement airfoil is reduced by about 8% compared to the baseline configuration.