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

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.480-485
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• 1993

A method for obtaining optimal orbital maneuvers of a space vehicle has been developed by combining feedback linearization method with the elegance of the Lambert's theorem. To obtain solutions to nonlinear orbital maneuver problems. The full nonlinear equations of motion for space vehicle in polar coordinate system are transformed exactly into a controllable linear set in Brunovsky canonical form by using feedback linearization by choosing position vector as fully observable output vector. These equations are used to pose a linear optimal tracking problem with a solutions to Lambert's problem and a linear analytical solution of continuous low thrust problem as reference trajectories.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.2
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• pp.183-192
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• 2013

This paper presents formation reconfiguration using impulsive control input for spacecraft formation flying. Spacecraft in a formation should change the formation size and/or geometry according to the mission requirements and space environment. To modify the formation radius and geometry with respect to the leader spacecraft, the follower spacecraft generates additional control inputs; the two impulsive control inputs are general control type of the spacecraft system. For the impulsive control input, Lambert's problem is modified to construct the transfer orbit in relative motion, given two position vectors at the initial and final time. Moreover, the numerical simulation results show the transfer trajectories to resize the formation radius in the radial/along-track plane formation and in the along-track/cross-track plane formation. In addition, the maneuver characteristics are described by comparing the differential orbital elements between the reference orbit and transfer orbit in the radial/along-track plane formation and along-track/cross-track plane formation.

• The Journal of the Acoustical Society of Korea
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• v.34 no.3
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• pp.184-191
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• 2015

In this paper, a normal mode reverberation model for a range-independent environment of shallow water is proposed to calculate the reverberation level in the low-frequency range. Normal mode is used to calculate the acoustic energy propagating from the source to the scattering area and from the scattering area to the receiver. Each mode is decomposed into up and down going waves to consider scattering strength at the scattering area. The scattering functional form combines Lambert's law with a Gaussian-like term near the specular direction based on Kirchhoff approximation considering bottom condition. For verification of the suggested model, the result is relatively compared to several solutions of the problem XI and XV in the Reverberation Modeling Workshop I sponsored by the US Office of Naval Research.

• Journal of the Korean Society of Propulsion Engineers
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• v.13 no.4
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• pp.36-44
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• 2009

Spray cross-section was measured by the Optical Line Patternator (OLP) and Optical Tomography at high ambient pressure. The laser line beam passed through the spray region, then Mie scattered signal and transmitted light were captured. The measured signal was processed to obtain a distribution of attenuation coefficient in spray cross-section. Beer-Lambert's law and mathematical reconstruction methods were used to reconstruct the distribution of attenuation coefficient. Spray became dense at high pressure and attenuation of scattered signal occurred seriously. OLP method, which uses Mie scattered signal, showed limit in compensating attenuation problem in dense spray region. Optical tomography reconstructed spray cross-section well, from transmission rate of light penetrating spray region.