• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.38 no.7
• /
• pp.684-692
• /
• 2010

Based on the planar restricted three body problem formulation, optimized trajectories for the Earth-Moon transfer are obtained. Mixed impulsive and continuous thrust are assumed to be used, respectively, during the Earth departure and Earth-Moon transfer/Moon capture phases. The continuous, dynamic trajectory optimization problem is reformulated in the form of discrete optimization problem by using the method of direct transcription and collocation, and then is solved using the nonlinear programming software. Representative results show that the shape of optimized trajectory near the Earth departure and the Moon capture phases is dependent upon the relative weight between the impulsive and the continuous thrust.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.39 no.11
• /
• pp.1021-1032
• /
• 2011

This paper presents the results of a parametric study for the design of optimal Earth-Moon transfer trajectory using mixed impulsive and continuous thrust. Various types of the optimal Earth-Moon transfer trajectories were designed by adjusting the relative weight between the impulsive and the continuous thrust, and flight time. Two very different transfer trajectories can be obtained by different combination of design parameters. Furthermore, it was found that all thus designed trajectories permit the ballistic capture by the Moon gravity. Finally, the required thrust profiles are presented and analyzed in detail.

• Journal of Astronomy and Space Sciences
• /
• v.28 no.3
• /
• pp.203-216
• /
• 2011

To prepare for a future Korean lunar orbiter mission, semi-optimal lunar capture orbits using finite thrust are designed and analyzed. Finite burn delta-V losses during lunar capture sequence are also analyzed by comparing those with values derived with impulsive thrusts in previous research. To design a hypothetical lunar capture sequence, two different intermediate capture orbits having orbital periods of about 12 hours and 3.5 hours are assumed, and final mission operation orbit around the Moon is assumed to be 100 km altitude with 90 degree of inclination. For the performance of the on-board thruster, three different performances (150 N with $I_{sp}$ of 200 seconds, 300 N with $I_{sp}$ of 250 seconds, 450 N with $I_{sp}$ of 300 seconds) are assumed, to provide a broad range of estimates of delta-V losses. As expected, it is found that the finite burn-arc sweeps almost symmetric orbital portions with respect to the perilune vector to minimize the delta-Vs required to achieve the final orbit. In addition, a difference of up to about 2% delta-V can occur during the lunar capture sequences with the use of assumed engine configurations, compared to scenarios with impulsive thrust. However, these delta-V losses will differ for every assumed lunar explorer's on-board thrust capability. Therefore, at the early stage of mission planning, careful consideration must be made while estimating mission budgets, particularly if the preliminary mission studies were assumed using impulsive thrust. The results provided in this paper are expected to lead to further progress in the design field of Korea's lunar orbiter mission, particularly the lunar capture sequences using finite thrust.

• Journal of Astronomy and Space Sciences
• /
• v.15 no.1
• /
• pp.235-244
• /
• 1998

The solutions of orbital maneuver problem using the sliding mode control in the presence of the erath gravitational perturbations is obtained. Especially, the optimization of consuming fuel for maneuver is performed. The impulsive solution to Lambert's problem using the combined equation method to minimize total ${\Delta}V is used for the desired orbit and the maneuver times. Two-step sliding mode control method is introduced for satisfying the boundary conditions of finite-thrust rendezvous problem at the end of maneuver time. Using the new approach to the orbit maneuver problem, two-step sliding mode control, orbit maneuvers are processed. The solutions to a rendezvous using the optimal control are obtained, and they are compared to the results by two-step sliding control.According to the new approach for orbit maneuver, the thrust-coast-thrust type controller is obtained to make satellite to track desired Lambert's orbit, and the total ${\Delta}V$ required for maneuver is resonable in comparison with the impulsive solution to Lambert's problem. The final state variables, also are close to the boundary conditions at the end of maneuver times.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.38 no.10
• /
• pp.998-1011
• /
• 2010

For preparing Korean lunar missions, an Earth-Moon transfer trajectory is designed and analyzed using finite thrust. To be a more realistic scenario, kick motor's performance which is used for TLI (Trans Lunar Injection) maneuver is assumed to have a certain maximum capability. Under this assumption, optimal Earth-Moon transfer trajectory analysis is made from the beginning of Earth departure to the final lunar closest approach. As a results, optimal Earth-Moon transfer trajectory solutions with finite thrust are compared to those of designed with impulsive thrust in previous study. It is confirmed that if the trajectory solutions derived with impulsive burn is directly applied to estimate the finite burn trajectory solutions, careful consideration for finite burn losses must be paid as for TLI maneuver. Presented algorithm and various results will give numerous insights into the future Korea's Lunar missions using finite thrust engines.

• The Bulletin of The Korean Astronomical Society
• /
• v.37 no.2
• /
• pp.160.1-160.1
• /
• 2012

We present an alternative approach for satellite formation reconfiguration by an optimal impulsive-thrust strategy to minimize the total characteristic velocity in a near-circular-orbit. Linear transformation decouples the Hill-Clohessy-Wiltshire(HCW) dynamics into a new block-diagonal system matrix consisting of 1-dimensional harmonic oscillator and 2-dimensional subsystem. In contrast to a solution based on the conventional primer vector theory, the optimal solution and the necessary conditions are represented as times and directions of impulses. New analytical expression of the total characteristic velocity is found for each sub systems under general boundary conditions including transfer time constraint. To minimize the total characteristic velocity, necessary conditions for times and directions of impulses are analytically solved. While the solution to the 1-dimensional harmonic oscillator has been found, the solution to the 2-dimensional subsystem is currently under construction. Our approach is expected to be applicable to more challenging problems.

• Bulletin of the Korean Space Science Society
• /
• 2008.10a
• /
• pp.25.3-26
• /
• 2008

The direct way to the moon is to start from the parking orbit by using impulsive thruster In previous domestic research, the direct way has been studied by using a single impulsive shot. However, when a single impulsive shot occurs to go into a Translunar orbit, gravity losses occur because thruster is not impulsive shot but the finite burns and it causes the gravity losses. To make up for the weak point of a single impulsive shot, this paper divides TLI (Trans Lunar Injection) into several small burns. Therefore, departure loop trajectory and the Translunar trajectory. This method is useful not only to reduce the gravity losses but also to check the condition of satellite. By using this method, this paper demostrates the optimized trajectory from Earth parking orbit to lunar mission orbit which minimizes the fuel, and the SNOPT (Sparse Nonlinear OPTimizer software) is used to find optimal solution. Also, this paper provides lunar mission profile which includes the mission schedule when TLI, LOI (Lunar Orbit Insertion) maneuvers occur, a mount of fuel when thruster is used and other mission parameters.

• Structural Engineering and Mechanics
• /
• v.50 no.3
• /
• pp.287-304
• /
• 2014

A computer based iterative numerical procedure has been developed to analyse reinforced high strength concrete columns subjected to horizontal wave loads and eccentric vertical load by taking the material, geometrical and wave load non-linearity into account. The behaviour of the column has been assumed, to be represented by Moment-Thrust-Curvature relationship of the column cross-section. The formulated computer program predicts horizontal load versus deflection behaviour of a column up to failure. The developed numerical model has been applied to analyse several column specimens of various slenderness, structural properties and axial load ratios, tested by other researchers. The predicted values are having a better agreement with experimental results. A simplified user friendly hydrodynamic load model has been developed based on Morison equation supplemented with a wave slap term to predict the high frequency non-linear impulsive hydrodynamic loads arising from steep waves, known as ringing loads. A computer program has been formulated based on the model to obtain the wave loads and non-dimensional wave load coefficients for all discretised nodes, along the length of column from instantaneous free water surface to bottom of the column at mud level. The columns of same size and material properties but having different slenderness ratio are analysed by the developed numerical procedure for the simulated wave loads under various vertical thrust. This paper discusses the results obtained in detail and effect of slenderness in resisting wave loads under various vertical thrust.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.38 no.2
• /
• pp.141-149
• /
• 2010

This paper contains impulsive maneuver which considers fuel consumption balance of chief satellite and deputy satellite in satellite formation flying. Thrust input is obtained by Lagrange' Multiplier method which is constructed by cost function with weight parameter of each satellite. Energy matching constraint is applied for boundedness of relative orbit, and theoretical solutions are verified by simulation results. Simulations are divided into two scenarios, with or without air-drag effect. This paper's results are expected to be used in real satellite formation flying, when fuel-balancing impulsive maneuver for relative orbit boundedness is needed.

• Journal of Astronomy and Space Sciences
• /
• v.26 no.2
• /
• pp.171-186
• /
• 2009

Various Earth-Moon transfer trajectories are designed and analyzed to prepare the future Korea's Lunar missions. Minimum fuel trajectory solutions are obtained for the departure year of 2017, 2020, 2022, and every required mission phases are analyzed from Earth departure to the final lunar mission orbit. N-body equations of motion are formulated which include the gravitational effect of the Sun, Earth and Moon. In addition, accelerations due to geopotential harmonics, Lunar J2 and solar radiation pressures are considered. Impulsive high thrust is assumed as the main thrusting method of spacecraft with launcher capability of KSLV-2 which is planned to be developed. For the method of injecting a spacecraft into a trans Lunar trajectory, both direct shooting from circular parking orbit and shooting from the multiple elliptical intermediate orbits are adapted, and their design results are compared and analyzed. In addition, spacecraft's visibility from Deajeon ground station are constrained to see how they affect the magnitude of TLI(Trans Lunar Injection) maneuver. The results presented in this paper includes launch opportunities, required optimal maneuver characteristics for each mission phase as well as the trajectory characteristics and numerous related parameters. It is confirmed that the final mass of Korean lunar explorer strongly depends onto the initial parking orbit's altitude and launcher's capability, rather than mission start time.