Automatic algorithm for accurate numerical gradient calculation in general and complex spacecraft trajectories

dc.contributor.advisorOcampo, Cesaren
dc.contributor.committeeMemberHull, David G.en
dc.creatorRestrepo Gómez, Ricardo León.en
dc.date.accessioned2012-02-21T15:05:54Zen
dc.date.available2012-02-21T15:05:54Zen
dc.date.issued2010-12en
dc.date.submittedDecember 2010en
dc.date.updated2012-02-21T15:06:01Zen
dc.descriptiontexten
dc.description.abstractAn automatic algorithm for accurate numerical gradient calculations has been developed. The algorithm is based on both finite differences and Chebyshev interpolation approximations. The novelty of the method is an automated tuning of the step size perturbation required for both methods. This automation guaranties the best possible solution using these approaches without the requirement of user inputs. The algorithm treats the functions as a black box, which makes it extremely useful when general and complex problems are considered. This is the case of spacecraft trajectory design problems and complex optimization systems. An efficient procedure for the automatic implementation is presented. Several examples based on an Earth-Moon free return trajectory are presented to validate and demonstrate the accuracy of the method. A state transition matrix (STM) procedure is developed as a reference for the validation of the method.en
dc.description.departmentAerospace Engineeringen
dc.format.mimetypeapplication/pdfen
dc.identifier.slug2152/ETD-UT-2010-12-2624en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2010-12-2624en
dc.language.isoengen
dc.subjectNumerical derivativesen
dc.subjectFinite differenceen
dc.subjectOptimization systemsen
dc.subjectTrajectory designen
dc.subjectState transition matrixen
dc.subjectChebyshev interpolationen
dc.titleAutomatic algorithm for accurate numerical gradient calculation in general and complex spacecraft trajectoriesen
dc.type.genrethesisen
thesis.degree.departmentAerospace Engineeringen
thesis.degree.disciplineAerospace Engineeringen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelMastersen
thesis.degree.nameMaster of Science in Engineeringen

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