{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/8608"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/8608","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"A Legendre Pseudospectral Method for rapid optimization of launch vehicle trajectories","abstract":"A Legendre Pseudospectral Method for launch vehicle trajectory optimization, pro­ posed by Mike Ross and Fariba Fahroo of the Naval Postgraduate School, is presented and applied successfully to several launch problems. The method uses a Legendre pseudospectral differentiation matrix to discretize nonlinear differential equations (such as the equations of motion) into nonlinear algebraic equations. The equations are then posed in the form of a nonlinear optimization problem and solved numerically. The method is demonstrated to work very well with both continuous and discontinuous states and controls. The method is applied to the following launch problems: the single-stage and two-stage Goddard problem; a simplified, single-stage, two-dimensional launch problem; and a two-stage, three-dimensional launch problem. A technique for reducing the size of problems with second order differential equations is presented and applied. This technique is shown to increase the speed of convergence of some problems. A predictive guidance algorithm demonstrates the feasibility of using the method to find both open- and closed-loop controls for a single-stage, three dimensional launch problem. The effects of different aerodynamic models between the optimizer and the \"real\" simulation are briefly analyzed. A number of issues that need to be resolved before the algorithm can be used in-flight for closed-loop guidance are described","abstract_html":"A Legendre Pseudospectral Method for launch vehicle trajectory optimization, pro­ posed by Mike Ross and Fariba Fahroo of the Naval Postgraduate School, is presented and applied successfully to several launch problems. The method uses a Legendre pseudospectral differentiation matrix to discretize nonlinear differential equations (such as the equations of motion) into nonlinear algebraic equations. The equations are then posed in the form of a nonlinear optimization problem and solved numerically. The method is demonstrated to work very well with both continuous and discontinuous states and controls. The method is applied to the following launch problems: the single-stage and two-stage Goddard problem; a simplified, single-stage, two-dimensional launch problem; and a two-stage, three-dimensional launch problem. A technique for reducing the size of problems with second order differential equations is presented and applied. This technique is shown to increase the speed of convergence of some problems. A predictive guidance algorithm demonstrates the feasibility of using the method to find both open- and closed-loop controls for a single-stage, three dimensional launch problem. The effects of different aerodynamic models between the optimizer and the "real" simulation are briefly analyzed. A number of issues that need to be resolved before the algorithm can be used in-flight for closed-loop guidance are described","abstract_has_math":false,"creators":["Rea, Jeremy Ryan, 1975-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics.","school":null,"contributors":[],"advisors":["I. Michael Ross, Richard E. Phillips and John J. Deyst."],"committee_chairs":[],"committee_members":[],"year":2001,"date_issued":"2001","date_published":"2001","updated_at":"2026-07-22T22:20:52Z","subjects":["Aeronautics and Astronautics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/8608","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["I. Michael Ross, Richard E. Phillips and John J. Deyst."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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The method uses a Legendre pseudospectral differentiation matrix to discretize nonlinear differential equations (such as the equations of motion) into nonlinear algebraic equations. The equations are then posed in the form of a nonlinear optimization problem and solved numerically. The method is demonstrated to work very well with both continuous and discontinuous states and controls. The method is applied to the following launch problems: the single-stage and two-stage Goddard problem; a simplified, single-stage, two-dimensional launch problem; and a two-stage, three-dimensional launch problem. A technique for reducing the size of problems with second order differential equations is presented and applied. This technique is shown to increase the speed of convergence of some problems. A predictive guidance algorithm demonstrates the feasibility of using the method to find both open- and closed-loop controls for a single-stage, three dimensional launch problem. 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The method is demonstrated to work very well with both continuous and discontinuous states and controls. The method is applied to the following launch problems: the single-stage and two-stage Goddard problem; a simplified, single-stage, two-dimensional launch problem; and a two-stage, three-dimensional launch problem. A technique for reducing the size of problems with second order differential equations is presented and applied. This technique is shown to increase the speed of convergence of some problems. A predictive guidance algorithm demonstrates the feasibility of using the method to find both open- and closed-loop controls for a single-stage, three dimensional launch problem. The effects of different aerodynamic models between the optimizer and the \"real\" simulation are briefly analyzed. 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