Many problems in aeronautics can be described in terms of nonlinear systems of equations. Carleman developed a technique to linearize such equations that could lead to analytical solutions of nonlinear problems. Nonlinear problems are difficult to solve in closed form and therefore the construction of such solutions is usually nontrivial. This thesis will apply the Carleman linearization technique to three model problems: a two-degree of-freedom (2DOF) ballistic trajectory, Blasius' boundary layer, and Van der Pol's equation and evaluate how well the technique can adequately approximate the solutions of these ordinary differential equations.
","abstract_html":"<p>Many problems in aeronautics can be described in terms of nonlinear systems of equations. Carleman developed a technique to linearize such equations that could lead to analytical solutions of nonlinear problems. Nonlinear problems are difficult to solve in closed form and therefore the construction of such solutions is usually nontrivial. This thesis will apply the Carleman linearization technique to three model problems: a two-degree of-freedom (2DOF) ballistic trajectory, Blasius' boundary layer, and Van der Pol's equation and evaluate how well the technique can adequately approximate the solutions of these ordinary differential equations.</p>","abstract_has_math":false,"creators":["Gaude, Brian William"],"institution":null,"degree_name":"Master of Aeronautical Science","degree_level":"Thesis - Open Access","degree_discipline":"Aeronautical Science","degree_department":null,"school":null,"contributors":["Richard S. Baty","Roy S. Baty","John C. Hogan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2001,"date_issued":"2001-04-01T08:00:00Z","date_published":"2001-04-01T08:00:00Z","updated_at":"2026-07-27T19:25:23Z","subjects":["nonlinear","aeronautical","Carleman","linearization","Aerospace Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/db-theses/307","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Richard S. Baty","Roy S. Baty","John C. Hogan"]},{"key":"dc:creator","label":"Author","values":["Gaude, Brian William"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Aeronautical Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Aeronautical Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["nonlinear","aeronautical","Carleman","linearization","Aerospace Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/db-theses/307"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Many problems in aeronautics can be described in terms of nonlinear systems of equations. Carleman developed a technique to linearize such equations that could lead to analytical solutions of nonlinear problems. Nonlinear problems are difficult to solve in closed form and therefore the construction of such solutions is usually nontrivial. This thesis will apply the Carleman linearization technique to three model problems: a two-degree of-freedom (2DOF) ballistic trajectory, Blasius' boundary layer, and Van der Pol's equation and evaluate how well the technique can adequately approximate the solutions of these ordinary differential equations.
"]},{"key":"dc:title","label":"Title","values":["Solving Nonlinear Aeronautical Problems Using the Carleman Linearization Method"]}]}],"canonical_facts":{"dc:contributor":["Richard S. Baty","Roy S. Baty","John C. Hogan"],"dc:creator":["Gaude, Brian William"],"dc:description.abstract":["Many problems in aeronautics can be described in terms of nonlinear systems of equations. Carleman developed a technique to linearize such equations that could lead to analytical solutions of nonlinear problems. Nonlinear problems are difficult to solve in closed form and therefore the construction of such solutions is usually nontrivial. This thesis will apply the Carleman linearization technique to three model problems: a two-degree of-freedom (2DOF) ballistic trajectory, Blasius' boundary layer, and Van der Pol's equation and evaluate how well the technique can adequately approximate the solutions of these ordinary differential equations.
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