{"id":"https://openalex.org/W2107209939","doi":"https://doi.org/10.1109/tcsi.2009.2035416","title":"Dirac Structures in Pseudo-Gradient Systems With an Emphasis on Electrical Networks","display_name":"Dirac Structures in Pseudo-Gradient Systems With an Emphasis on Electrical Networks","publication_year":2010,"publication_date":"2010-01-08","ids":{"openalex":"https://openalex.org/W2107209939","doi":"https://doi.org/10.1109/tcsi.2009.2035416","mag":"2107209939"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2009.2035416","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2009.2035416","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022798705","display_name":"Jon Pierre Fortney","orcid":null},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]},{"id":"https://openalex.org/I4210116222","display_name":"Northrop Grumman (United Kingdom)","ror":"https://ror.org/02qjwrc97","country_code":"GB","type":"company","lineage":["https://openalex.org/I2948394018","https://openalex.org/I4210116222"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"Jon Pierre Fortney","raw_affiliation_strings":["Department of Mathematics, Arizona State University, Tempe, AZ, USA","Vinnell Arabia, a subsidiary, Northrop Grumman Corporation, Riyadh, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Vinnell Arabia, a subsidiary, Northrop Grumman Corporation, Riyadh, Saudi Arabia","institution_ids":["https://openalex.org/I4210116222"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022798705"],"corresponding_institution_ids":["https://openalex.org/I4210116222","https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":0.7226,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7837089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"57","issue":"7","first_page":"1732","last_page":"1745"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12763","display_name":"ATP Synthase and ATPases Research","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11445","display_name":"Origins and Evolution of Life","score":0.9381999969482422,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cotangent-bundle","display_name":"Cotangent bundle","score":0.811858594417572},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.7661815881729126},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6244878768920898},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6169038414955139},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5490777492523193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5445705652236938},{"id":"https://openalex.org/keywords/superintegrable-hamiltonian-system","display_name":"Superintegrable Hamiltonian system","score":0.49791955947875977},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4849729537963867},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.47354835271835327},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.45177099108695984},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.41700810194015503},{"id":"https://openalex.org/keywords/foliation","display_name":"Foliation (geology)","score":0.41631361842155457},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":0.4116325378417969},{"id":"https://openalex.org/keywords/covariant-hamiltonian-field-theory","display_name":"Covariant Hamiltonian field theory","score":0.4116085171699524},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3284684419631958},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30400335788726807},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.23464924097061157},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21360090374946594},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1444576382637024},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.10724207758903503}],"concepts":[{"id":"https://openalex.org/C7979169","wikidata":"https://www.wikidata.org/wiki/Q1142143","display_name":"Cotangent bundle","level":3,"score":0.811858594417572},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.7661815881729126},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6244878768920898},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6169038414955139},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5490777492523193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5445705652236938},{"id":"https://openalex.org/C177715462","wikidata":"https://www.wikidata.org/wiki/Q7643453","display_name":"Superintegrable Hamiltonian system","level":4,"score":0.49791955947875977},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4849729537963867},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.47354835271835327},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.45177099108695984},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.41700810194015503},{"id":"https://openalex.org/C168425004","wikidata":"https://www.wikidata.org/wiki/Q525802","display_name":"Foliation (geology)","level":3,"score":0.41631361842155457},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.4116325378417969},{"id":"https://openalex.org/C109798219","wikidata":"https://www.wikidata.org/wiki/Q25304038","display_name":"Covariant Hamiltonian field theory","level":3,"score":0.4116085171699524},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3284684419631958},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30400335788726807},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.23464924097061157},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21360090374946594},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1444576382637024},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.10724207758903503},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C26687426","wikidata":"https://www.wikidata.org/wiki/Q47069","display_name":"Metamorphic rock","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C17409809","wikidata":"https://www.wikidata.org/wiki/Q161764","display_name":"Geochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2009.2035416","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2009.2035416","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1606202192","https://openalex.org/W1720609403","https://openalex.org/W1998048993","https://openalex.org/W2001290675","https://openalex.org/W2008024201","https://openalex.org/W2072287784","https://openalex.org/W2088373274","https://openalex.org/W2098400868","https://openalex.org/W2099481648","https://openalex.org/W2104624259","https://openalex.org/W2105970071","https://openalex.org/W2107263628","https://openalex.org/W2126234893","https://openalex.org/W2136722879","https://openalex.org/W2138516376","https://openalex.org/W2140823649","https://openalex.org/W2147600547","https://openalex.org/W2151269244","https://openalex.org/W2151642424","https://openalex.org/W2151777071","https://openalex.org/W2155283338","https://openalex.org/W2155881450","https://openalex.org/W2562183967","https://openalex.org/W4213284467","https://openalex.org/W4243855827","https://openalex.org/W4247700768","https://openalex.org/W4255427351"],"related_works":["https://openalex.org/W2010097811","https://openalex.org/W2345020298","https://openalex.org/W2059357495","https://openalex.org/W1484362870","https://openalex.org/W2889581240","https://openalex.org/W2089815508","https://openalex.org/W36657179","https://openalex.org/W4312106975","https://openalex.org/W3123072352","https://openalex.org/W4367020943"],"abstract_inverted_index":{"The":[0],"relationship":[1,58],"between":[2,59],"implicitly":[3,22],"defined":[4,23],"Hamiltonian":[5,20,66,82],"systems":[6,9],"and":[7,63],"pseudo-gradient":[8,41,62,108],"is":[10,13,76,97],"investigated.":[11],"It":[12],"shown":[14],"that":[15],"under":[16],"certain":[17],"conditions":[18],"a":[19,27,40,87,98,107],"system,":[21],"with":[24],"respect":[25],"to":[26,38,86,106],"Dirac":[28],"structure":[29],"on":[30,43],"the":[31,44,48,52,57,60,64,80,90],"state":[32,53],"space":[33],"manifold,":[34],"can":[35],"be":[36],"used":[37],"generate":[39],"system":[42,83],"Lagrangian":[45,91],"submanifold":[46,92],"of":[47,51,68,89],"cotangent":[49],"bundle":[50],"space.":[54],"This":[55],"elucidates":[56],"Smale":[61],"Bloch-Couch":[65],"formulations":[67],"lossless":[69],"circuit":[70],"dynamics.":[71],"A":[72],"more":[73],"general":[74],"situation":[75],"also":[77],"considered":[78],"where":[79],"implicit":[81],"gives":[84,104],"rise":[85,105],"foliation":[88],"in":[93,102],"which":[94,101],"each":[95],"leaf":[96],"pseudo-Riemannian":[99],"manifold":[100],"turn":[103],"system.":[109]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}