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

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

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dc.contributor.advisor Ocampo, Cesar
dc.creator Restrepo, Ricardo Leon
dc.date.accessioned 2012-02-21T15:05:54Z
dc.date.available 2012-02-21T15:05:54Z
dc.date.created 2010-12
dc.date.issued 2012-02-21
dc.date.submitted December 2010
dc.identifier.uri http://hdl.handle.net/2152/ETD-UT-2010-12-2624
dc.description.abstract An 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.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subject Numerical derivatives
dc.subject Finite difference
dc.subject Optimization systems
dc.subject Trajectory design
dc.subject State transition matrix
dc.subject Chebyshev interpolation
dc.title Automatic algorithm for accurate numerical gradient calculation in general and complex spacecraft trajectories
dc.date.updated 2012-02-21T15:06:01Z
dc.identifier.slug 2152/ETD-UT-2010-12-2624
dc.contributor.committeeMember Hull, David G.
dc.description.department Aerospace Engineering
dc.type.genre thesis
dc.type.material text
thesis.degree.department Aerospace Engineering
thesis.degree.discipline Aerospace Engineering
thesis.degree.grantor University of Texas at Austin
thesis.degree.level Masters
thesis.degree.name Master of Science in Engineering

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