{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/76506"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/76506","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Singular trajectories in airplane cruise-dash optimization","abstract":"The problem of determining cruise-dash trajectories is examined for the case of time-fuel optimization using a linear combination of time and fuel as the performance index. These trajectories consist of a transient arc followed by a steady-state arc. For cases where the steady-state arc is flown with full throttle the associated skeletal transient trajectories are also flown with full throttle, and approach the cruise-dash points monotonically in an asymptotic fashion. When the steady-state arc is flown at an intermediate throttle setting, the transient trajectories follow a singular control law and exhibit a complex structure that is different from the full-throttle transients. Singular transients in the vicinity of singular cruise-dash points are confined to a bounded singular surface. In state-space these trajectories trace out asymptotic spirals on the singular surface as they approach the steady-state arc. If the initial operating point lies outside the singular surface, then the transient trajectories are composites consisting of a full-throttle or zero-throttle segment flown until the singular surface is met, followed by a singular segment that fairs into the cruise-dash point. Addressing the question of optimality of the steady-state arc, it was found that although steady-state cruise fails a Jacobi-type condition, steady-state cruise-dash can satisfy this condition if the emphasis on time is sufficiently large. The outcome of the Jacobi-type test appears to be connected with the eigenstructure of the linearized state-adjoint system.","abstract_html":"The problem of determining cruise-dash trajectories is examined for the case of time-fuel optimization using a linear combination of time and fuel as the performance index. These trajectories consist of a transient arc followed by a steady-state arc. For cases where the steady-state arc is flown with full throttle the associated skeletal transient trajectories are also flown with full throttle, and approach the cruise-dash points monotonically in an asymptotic fashion. When the steady-state arc is flown at an intermediate throttle setting, the transient trajectories follow a singular control law and exhibit a complex structure that is different from the full-throttle transients. Singular transients in the vicinity of singular cruise-dash points are confined to a bounded singular surface. In state-space these trajectories trace out asymptotic spirals on the singular surface as they approach the steady-state arc. If the initial operating point lies outside the singular surface, then the transient trajectories are composites consisting of a full-throttle or zero-throttle segment flown until the singular surface is met, followed by a singular segment that fairs into the cruise-dash point. Addressing the question of optimality of the steady-state arc, it was found that although steady-state cruise fails a Jacobi-type condition, steady-state cruise-dash can satisfy this condition if the emphasis on time is sufficiently large. The outcome of the Jacobi-type test appears to be connected with the eigenstructure of the linearized state-adjoint system.","abstract_has_math":false,"creators":["Bilimoria, Karl D."],"institution":"Virginia Polytechnic Institute and State University","degree_name":"PH. D.","degree_level":"doctoral","degree_discipline":"Aerospace Engineering","degree_department":"Aerospace Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Cliff, Eugene M."],"committee_members":["Kelley, Henry J.","Lutze, Frederick H.","Stalford, Harold L.","Marchman, James F."],"year":1987,"date_issued":"1987","date_published":"1987","updated_at":"2026-07-22T22:19:27Z","subjects":[],"languages":["en_US"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/76506","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Cliff, Eugene M."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Kelley, Henry J.","Lutze, Frederick H.","Stalford, Harold L.","Marchman, James F."]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace Engineering"]},{"key":"dc:creator","label":"Author","values":["Bilimoria, Karl D."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-03-10T21:54:48Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-03-10T21:54:48Z"]},{"key":"dc:date.issued","label":"Date","values":["1987"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute and State University"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["PH. 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For cases where the steady-state arc is flown with full throttle the associated skeletal transient trajectories are also flown with full throttle, and approach the cruise-dash points monotonically in an asymptotic fashion. When the steady-state arc is flown at an intermediate throttle setting, the transient trajectories follow a singular control law and exhibit a complex structure that is different from the full-throttle transients. Singular transients in the vicinity of singular cruise-dash points are confined to a bounded singular surface. In state-space these trajectories trace out asymptotic spirals on the singular surface as they approach the steady-state arc. If the initial operating point lies outside the singular surface, then the transient trajectories are composites consisting of a full-throttle or zero-throttle segment flown until the singular surface is met, followed by a singular segment that fairs into the cruise-dash point. Addressing the question of optimality of the steady-state arc, it was found that although steady-state cruise fails a Jacobi-type condition, steady-state cruise-dash can satisfy this condition if the emphasis on time is sufficiently large. The outcome of the Jacobi-type test appears to be connected with the eigenstructure of the linearized state-adjoint system."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["PH. D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Singular trajectories in airplane cruise-dash optimization"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Cliff, Eugene M."],"dc:contributor.committeemember":["Kelley, Henry J.","Lutze, Frederick H.","Stalford, Harold L.","Marchman, James F."],"dc:contributor.department":["Aerospace Engineering"],"dc:creator":["Bilimoria, Karl D."],"dc:date.accessioned":["2017-03-10T21:54:48Z"],"dc:date.available":["2017-03-10T21:54:48Z"],"dc:date.issued":["1987"],"dc:description.abstract":["The problem of determining cruise-dash trajectories is examined for the case of time-fuel optimization using a linear combination of time and fuel as the performance index. These trajectories consist of a transient arc followed by a steady-state arc. For cases where the steady-state arc is flown with full throttle the associated skeletal transient trajectories are also flown with full throttle, and approach the cruise-dash points monotonically in an asymptotic fashion. When the steady-state arc is flown at an intermediate throttle setting, the transient trajectories follow a singular control law and exhibit a complex structure that is different from the full-throttle transients. Singular transients in the vicinity of singular cruise-dash points are confined to a bounded singular surface. In state-space these trajectories trace out asymptotic spirals on the singular surface as they approach the steady-state arc. If the initial operating point lies outside the singular surface, then the transient trajectories are composites consisting of a full-throttle or zero-throttle segment flown until the singular surface is met, followed by a singular segment that fairs into the cruise-dash point. Addressing the question of optimality of the steady-state arc, it was found that although steady-state cruise fails a Jacobi-type condition, steady-state cruise-dash can satisfy this condition if the emphasis on time is sufficiently large. The outcome of the Jacobi-type test appears to be connected with the eigenstructure of the linearized state-adjoint system."],"dc:description.degree":["PH. D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/76506"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute and State University"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Singular trajectories in airplane cruise-dash optimization"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["PH. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:27Z"}