{"id":"https://openalex.org/W7208768147","doi":"https://doi.org/10.48550/arxiv.2609.04084","title":"Transversality Conditions for Boundary Constraints Defined by Differential Equations","display_name":"Transversality Conditions for Boundary Constraints Defined by Differential Equations","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7208768147","doi":"https://doi.org/10.48550/arxiv.2609.04084"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04084","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04084","pdf_url":"https://arxiv.org/pdf/2609.04084","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.04084","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150047983","display_name":"Isaac M Ross","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ross, Isaac M","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5150047983"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9384999871253967,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9384999871253967,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10545","display_name":"Optimization and Variational Analysis","score":0.050700001418590546,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.002300000051036477,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/transversality-conditions","display_name":"transversality conditions","score":0.9980000257492065},{"id":"https://openalex.org/keywords/optimal-control","display_name":"optimal control","score":0.8500000238418579},{"id":"https://openalex.org/keywords/trajectory-optimization","display_name":"trajectory optimization","score":0.6869999766349792},{"id":"https://openalex.org/keywords/n-body-problem","display_name":"N-body problem","score":0.9570000171661377},{"id":"https://openalex.org/keywords/three-body-problem","display_name":"three-body problem","score":0.9739999771118164}],"concepts":[{"id":"https://openalex.org/C24167531","wikidata":"https://www.wikidata.org/wiki/Q2300767","display_name":"Transversality","level":2,"score":0.946399986743927},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7670000195503235},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5496000051498413},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5443000197410583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4975999891757965},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4449000060558319},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3919999897480011},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.39169999957084656},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.37310001254081726},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C2780528706","wikidata":"https://www.wikidata.org/wiki/Q1760485","display_name":"Seakeeping","level":3,"score":0.35760000348091125},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2858000099658966},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04084","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04084","pdf_url":"https://arxiv.org/pdf/2609.04084","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.04084","doi":"https://doi.org/10.48550/arxiv.2609.04084","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.04084","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04084","pdf_url":"https://arxiv.org/pdf/2609.04084","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208768147.pdf","grobid_xml":"https://content.openalex.org/works/W7208768147.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1970011640","https://openalex.org/W2074257829","https://openalex.org/W2773490535","https://openalex.org/W2888464273","https://openalex.org/W2897459454","https://openalex.org/W2908931612","https://openalex.org/W4224009911","https://openalex.org/W4249513058","https://openalex.org/W4310075952","https://openalex.org/W4362471655","https://openalex.org/W6944889523","https://openalex.org/W7202155794"],"related_works":["https://openalex.org/W1987160262","https://openalex.org/W7132610076","https://openalex.org/W2070635606","https://openalex.org/W2356682221","https://openalex.org/W103074373","https://openalex.org/W2060950509","https://openalex.org/W2004661573","https://openalex.org/W2607174411","https://openalex.org/W2086015428","https://openalex.org/W2346862455"],"abstract_inverted_index":{"What":[0],"are":[1,14,74,91,115,174,188],"the":[2,11,30,58,94,102,105,118,124,143,147,157,165,179,185],"transversality":[3,65,126],"conditions":[4,13,66,73,90,127],"for":[5,67],"an":[6],"optimal":[7,68],"control":[8,69],"problem":[9,187],"when":[10],"boundary":[12,72,89,148],"defined":[15,75],"by":[16,25],"differential":[17,79,88,149],"equations?":[18],"This":[19,151],"seemingly":[20],"bizarre":[21],"question":[22],"is":[23,36,57,140,153],"motivated":[24],"trajectory":[26],"optimization":[27],"problems":[28,42,70],"in":[29,43,49,76,97,171,184,190],"$N$-body":[31],"system.":[32],"The":[33,51,84,168],"question,":[34],"however,":[35],"more":[37],"fundamental":[38],"and":[39,63,111],"goes":[40],"beyond":[41],"astrodynamics":[44],"to":[45,142,164,181],"nonintegrable":[46],"dynamical":[47],"systems":[48],"general.":[50],"main":[52],"contribution":[53],"of":[54,60,78,87,93,107,120,146,160,178],"this":[55,98,172],"paper":[56,173],"development":[59],"generic":[61],"initial-":[62],"final-time":[64],"whose":[71],"terms":[77],"equations":[80],"with":[81,162],"side":[82],"conditions.":[83],"mathematical":[85],"definition":[86],"part":[92],"foundations":[95],"developed":[96,170],"paper.":[99],"To":[100],"support":[101],"new":[103,125],"fundamentals,":[104],"concept":[106],"coordinated/uncoordinated":[108],"clock":[109,122],"times":[110],"weak":[112,137],"adjoint":[113,138],"covectors":[114],"introduced.":[116],"In":[117],"case":[119],"uncoordinated":[121],"times,":[123],"reveal":[128],"that":[129],"there":[130],"exists":[131],"a":[132,136],"special":[133],"situation":[134],"where":[135],"covector":[139],"orthogonal":[141],"vector":[144],"field":[145],"equation.":[150],"condition":[152],"sharply":[154],"different":[155],"from":[156],"classical":[158],"statement":[159],"orthogonality":[161],"respect":[163],"endpoint":[166],"manifold.":[167],"theorems":[169,180],"generic.":[175],"An":[176],"application":[177],"several":[182],"cases":[183],"three-body":[186],"described":[189],"separate":[191],"papers.":[192]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-05T00:00:00"}
