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Using the Picard-Chebyshev Method to Solve Complex Problems in Space Sciences

Since enrolling in the Department of Mechanical and Aerospace Engineering at CSULB, Darin Koblick has authored over half a dozen technical papers pertaining to his research involving astrodynamics and Space Situational Awareness. His findings have been presented in many international technical venues which include: the American Institute of Aeronautics and Astronautics, the Massachusetts Institute of Technology, Lincoln Laboratories Space Control Conference, the International Conference on Computational & Experimental Engineering and Sciences, the Advanced Maui Optical and Space Surveillance Technologies Conference, and the International Mechanical Engineering Congress and Exposition.

Since working on his master’s thesis in 2012, Koblick, along with his doctoral advisor Dr. Praveen Shankar, has been investigating promising applications for the Modified Picard Chebyshev Method (MPCM), a perturbative approach to numerically solving ordinary differential equations. Recently, Koblick’s work involving the optimization of low thrust orbit maneuvers via the MPCM was accepted to a special edition journal issue of Computer Modeling in Engineering and Sciences (available later this year).

Koblick continues to rely on his experience as an aerospace professional, his education in CSULB’s Engineering & Industrial Applied Mathematics joint doctoral program with Claremont Graduate University, and his professional network to develop and analyze innovative techniques necessary for solving challenging technical problems in space sciences.

Graphic figure of the low thrust maneuver from a low Earth orbit. Details are explained in article text.

Figure: Optimized low thrust maneuver from a low Earth orbit (390 miles above sea level) to a Geostationary orbit (about 22,236 miles above sea level). This was found with the help of the Modified Picard-Chebyshev Method.

Series of graphs depicting Six Keplerian Orbital Elements over the full orbit maneuver sequence. Details are explained in article text.

Figure: Six Keplerian Orbital Elements over the full orbit maneuver sequence. Note that the Semi-major axis grows until GEO and the orbital inclination is reduced from 28.5 to 1 degree. The initial and final eccentricity values are kept near zero to ensure a circular orbit.

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