{"id":"https://openalex.org/W1468015989","doi":"https://doi.org/10.1137/130921908","title":"The Principle of Least Action and Fundamental Solutions of Mass-Spring and N-Body Two-Point Boundary Value Problems","display_name":"The Principle of Least Action and Fundamental Solutions of Mass-Spring and N-Body Two-Point Boundary Value Problems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1468015989","doi":"https://doi.org/10.1137/130921908","mag":"1468015989"},"language":"en","primary_location":{"id":"doi:10.1137/130921908","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130921908","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5069202152","display_name":"William M. McEneaney","orcid":"https://orcid.org/0000-0002-0576-9949"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William M. McEneaney","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004101031","display_name":"Peter M. Dower","orcid":"https://orcid.org/0000-0002-9791-7776"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter M. Dower","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8619,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.94062565,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"53","issue":"5","first_page":"2898","last_page":"2933"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9973999857902527,"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/mathematics","display_name":"Mathematics","score":0.8402616381645203},{"id":"https://openalex.org/keywords/action","display_name":"Action (physics)","score":0.6190392971038818},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5934983491897583},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5925171375274658},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5607497692108154},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4718765318393707},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4311518967151642},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4269155263900757},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41537585854530334},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.4150713384151459},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3787507712841034},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3146873712539673}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8402616381645203},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.6190392971038818},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5934983491897583},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5925171375274658},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5607497692108154},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4718765318393707},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4311518967151642},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4269155263900757},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41537585854530334},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.4150713384151459},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3787507712841034},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3146873712539673},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130921908","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130921908","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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":26,"referenced_works":["https://openalex.org/W573706636","https://openalex.org/W586948577","https://openalex.org/W644523282","https://openalex.org/W1487586009","https://openalex.org/W1488435683","https://openalex.org/W1494380031","https://openalex.org/W1574514837","https://openalex.org/W1577338488","https://openalex.org/W1964306305","https://openalex.org/W1966660110","https://openalex.org/W1970423963","https://openalex.org/W1975017621","https://openalex.org/W1981476333","https://openalex.org/W1985077192","https://openalex.org/W1997093580","https://openalex.org/W1998401686","https://openalex.org/W2002607811","https://openalex.org/W2018686874","https://openalex.org/W2049567323","https://openalex.org/W2059161794","https://openalex.org/W2065959526","https://openalex.org/W2073044650","https://openalex.org/W2101322491","https://openalex.org/W2163713673","https://openalex.org/W2404358657","https://openalex.org/W3111685920"],"related_works":["https://openalex.org/W1859185863","https://openalex.org/W4285537323","https://openalex.org/W2964126589","https://openalex.org/W1932159282","https://openalex.org/W4307691181","https://openalex.org/W3016225735","https://openalex.org/W1518875602","https://openalex.org/W2017412075","https://openalex.org/W2116748936","https://openalex.org/W2133690079"],"abstract_inverted_index":{"Two-point":[0],"boundary":[1,24],"value":[2,25,31],"problems":[3,26,32],"for":[4],"conservative":[5],"systems":[6],"are":[7,27,99],"studied":[8],"in":[9],"the":[10,13,38,47,69,95],"context":[11],"of":[12,37,91,104,106],"least":[14,70],"action":[15,71],"principle.":[16],"One":[17],"obtains":[18],"a":[19,42,57,79],"fundamental":[20,39],"solution,":[21],"whereby":[22],"two-point":[23],"converted":[28,77],"to":[29,46,78,93],"initial":[30],"via":[33],"an":[34,83,88],"idempotent":[35],"convolution":[36],"solution":[40],"with":[41],"cost":[43],"function":[44],"related":[45],"terminal":[48],"data.":[49],"The":[50,60],"classical":[51],"mass-spring":[52],"problem":[53,62,75],"is":[54,65,76],"included":[55],"as":[56,101],"simple":[58],"example.":[59],"$N$-body":[61],"under":[63],"gravitation":[64],"also":[66],"studied.":[67],"There,":[68],"principle":[72],"optimal":[73],"control":[74],"differential":[80],"game,":[81],"where":[82],"opposing":[84],"player":[85],"maximizes":[86],"over":[87],"indexed":[89,102],"set":[90],"quadratics":[92],"yield":[94],"gravitational":[96],"potential.":[97],"Solutions":[98],"obtained":[100],"sets":[103],"solutions":[105],"Riccati":[107],"equations.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}