{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/71209"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/71209","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Three-dimensional display of phase space diagrams","abstract":"Phase plane analysis of linear and nonlinear systems has been widely in recent years. These graphical displays give considerable insight into system response. A serious short coming of this procedure is the limitation to two dimensions. A third-order system must be studied on two, two-dimensional graphs or represented by a second-order mathematical approximation for the third-order system. For nonlinear systems employing relays, saturation, etc., the approximations must be made with care. In an effort to reduce discrepancies and improve the visualization of system response, this paper presents a method to obtain three-dimensional displays of system graphs. Third-order phase graphs of nonlinear and linear systems can be graphed directly without approximations. A discussion of the principles involved will be presented first. Then, analog and digital programs will be given. Finally, example problems will be discussed.","abstract_html":"Phase plane analysis of linear and nonlinear systems has been widely in recent years. These graphical displays give considerable insight into system response. A serious short coming of this procedure is the limitation to two dimensions. A third-order system must be studied on two, two-dimensional graphs or represented by a second-order mathematical approximation for the third-order system. For nonlinear systems employing relays, saturation, etc., the approximations must be made with care. In an effort to reduce discrepancies and improve the visualization of system response, this paper presents a method to obtain three-dimensional displays of system graphs. Third-order phase graphs of nonlinear and linear systems can be graphed directly without approximations. A discussion of the principles involved will be presented first. Then, analog and digital programs will be given. Finally, example problems will be discussed.","abstract_has_math":false,"creators":["English, Donald L."],"institution":"Virginia Polytechnic Institute","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Electrical Engineering","degree_department":"Electrical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1968,"date_issued":"1968","date_published":"1968","updated_at":"2026-07-22T22:18:55Z","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/10919/71209","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Electrical Engineering"]},{"key":"dc:creator","label":"Author","values":["English, Donald L."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-05-23T17:53:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-05-23T17:53:45Z"]},{"key":"dc:date.issued","label":"Date","values":["1968"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/71209"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Phase plane analysis of linear and nonlinear systems has been widely in recent years. These graphical displays give considerable insight into system response. A serious short coming of this procedure is the limitation to two dimensions. A third-order system must be studied on two, two-dimensional graphs or represented by a second-order mathematical approximation for the third-order system. For nonlinear systems employing relays, saturation, etc., the approximations must be made with care. In an effort to reduce discrepancies and improve the visualization of system response, this paper presents a method to obtain three-dimensional displays of system graphs. Third-order phase graphs of nonlinear and linear systems can be graphed directly without approximations. A discussion of the principles involved will be presented first. Then, analog and digital programs will be given. Finally, example problems will be discussed."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Three-dimensional display of phase space diagrams"]}]}],"canonical_facts":{"dc:contributor.department":["Electrical Engineering"],"dc:creator":["English, Donald L."],"dc:date.accessioned":["2016-05-23T17:53:45Z"],"dc:date.available":["2016-05-23T17:53:45Z"],"dc:date.issued":["1968"],"dc:description.abstract":["Phase plane analysis of linear and nonlinear systems has been widely in recent years. These graphical displays give considerable insight into system response. A serious short coming of this procedure is the limitation to two dimensions. A third-order system must be studied on two, two-dimensional graphs or represented by a second-order mathematical approximation for the third-order system. For nonlinear systems employing relays, saturation, etc., the approximations must be made with care. In an effort to reduce discrepancies and improve the visualization of system response, this paper presents a method to obtain three-dimensional displays of system graphs. Third-order phase graphs of nonlinear and linear systems can be graphed directly without approximations. A discussion of the principles involved will be presented first. Then, analog and digital programs will be given. Finally, example problems will be discussed."],"dc:description.degree":["Master of Science"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/71209"],"dc:language.iso":["en_US"],"dc:publisher":["Virginia Polytechnic Institute"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Three-dimensional display of phase space diagrams"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Electrical Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute"]},"updated_at":"2026-07-22T22:18:55Z"}