{"id":"https://openalex.org/W1535361766","doi":"https://doi.org/10.1109/cdc.2002.1184292","title":"Energy equipartition and the emergence of damping in lossless systems","display_name":"Energy equipartition and the emergence of damping in lossless systems","publication_year":2003,"publication_date":"2003-08-27","ids":{"openalex":"https://openalex.org/W1535361766","doi":"https://doi.org/10.1109/cdc.2002.1184292","mag":"1535361766"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2002.1184292","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2002.1184292","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.","raw_type":"proceedings-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/A5009770702","display_name":"Dennis S. Bernstein","orcid":"https://orcid.org/0000-0003-0399-3039"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D.S. Bernstein","raw_affiliation_strings":["Department of AeroSpace Engineering, University of Michigan, Ann Arbor, MI, USA","[Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI, USA]"],"affiliations":[{"raw_affiliation_string":"Department of AeroSpace Engineering, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"[Dept. of Aerosp. Eng., Michigan Univ., Ann Arbor, MI, USA]","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039306255","display_name":"Sanjay P. Bhat","orcid":"https://orcid.org/0000-0002-8595-6081"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S.P. Bhat","raw_affiliation_strings":["Department of AeroSpace Engineering, Indian Institute of Technology, Mumbai, India","Indian Inst. of Technology, Bombay"],"affiliations":[{"raw_affiliation_string":"Department of AeroSpace Engineering, Indian Institute of Technology, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Inst. of Technology, Bombay","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009770702"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":2.2945,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.87597311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"3","issue":null,"first_page":"2913","last_page":"2918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.994700014591217,"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"}},"topics":[{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.994700014591217,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equipartition-theorem","display_name":"Equipartition theorem","score":0.9651064872741699},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.6820982694625854},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6072606444358826},{"id":"https://openalex.org/keywords/lossless-compression","display_name":"Lossless compression","score":0.5175411105155945},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5079839825630188},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5019984245300293},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4912533164024353},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.48529666662216187},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4421481192111969},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3649367094039917},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2986980974674225},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28141605854034424},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09601348638534546}],"concepts":[{"id":"https://openalex.org/C99742106","wikidata":"https://www.wikidata.org/wiki/Q255996","display_name":"Equipartition theorem","level":3,"score":0.9651064872741699},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.6820982694625854},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6072606444358826},{"id":"https://openalex.org/C81081738","wikidata":"https://www.wikidata.org/wiki/Q55542","display_name":"Lossless compression","level":3,"score":0.5175411105155945},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5079839825630188},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5019984245300293},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4912533164024353},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.48529666662216187},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4421481192111969},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3649367094039917},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2986980974674225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28141605854034424},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09601348638534546},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"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/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2002.1184292","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2002.1184292","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 41st IEEE Conference on Decision and Control, 2002.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1499871105","https://openalex.org/W1966498078","https://openalex.org/W1972271786","https://openalex.org/W1972447015","https://openalex.org/W1984050667","https://openalex.org/W1987442494","https://openalex.org/W1996851673","https://openalex.org/W2003137566","https://openalex.org/W2005789397","https://openalex.org/W2007876331","https://openalex.org/W2022656677","https://openalex.org/W2080476921","https://openalex.org/W2087040380","https://openalex.org/W2091935636","https://openalex.org/W2094014274","https://openalex.org/W2104891404","https://openalex.org/W2124707072","https://openalex.org/W2145198445","https://openalex.org/W2461412242","https://openalex.org/W2527383467","https://openalex.org/W4300524207"],"related_works":["https://openalex.org/W2072691113","https://openalex.org/W2090923322","https://openalex.org/W2070195754","https://openalex.org/W2142627477","https://openalex.org/W2083385574","https://openalex.org/W2777849946","https://openalex.org/W3204217173","https://openalex.org/W4300815638","https://openalex.org/W2053120546","https://openalex.org/W2489761661"],"abstract_inverted_index":{"The":[0],"principle":[1],"of":[2,4,16,20,39,41,55,58,99,111,116,132,140,145,148,159],"equipartition":[3,115,131],"energy":[5,38,83,88,117,141],"is":[6,50],"usually":[7],"viewed":[8],"as":[9],"a":[10,72,97,112],"statistical":[11,67],"result":[12],"formulated":[13],"in":[14,108],"terms":[15],"the":[17,36,59,79,85,91,109,120,130,137,146,154],"probability":[18],"distribution":[19,139],"configurations,":[21],"that":[22,78,135],"is,":[23,136],"entropy.":[24],"In":[25],"this":[26],"paper":[27],"we":[28,95],"use":[29],"deterministic":[30],"linear":[31],"systems":[32,40],"techniques":[33],"to":[34,90],"analyze":[35],"vibrational":[37],"undamped":[42,74,102],"coupled":[43],"oscillators":[44,103],"with":[45,104],"identical":[46,101],"coupling.":[47,106],"Our":[48],"approach":[49],"based":[51],"on":[52,129],"time":[53,80],"averaging":[54],"squared":[56],"outputs":[57],"system":[60,122],"and":[61,66,76,84,124,156],"thus":[62],"avoids":[63],"both":[64],"recurrence":[65],"arguments.":[68],"We":[69,127,150],"first":[70],"consider":[71,96],"single":[73,113],"oscillator":[75,133],"show":[77],"averaged":[81],"potential":[82,125],"time-averaged":[86],"kinetic":[87,123],"converge":[89],"same":[92],"value.":[93],"Next,":[94],"collection":[98],"n":[100],"lossless":[105],"As":[107],"case":[110],"oscillator,":[114],"holds":[118],"for":[119,153],"total":[121],"energies.":[126],"focus":[128],"energy,":[134],"equal":[138],"among":[142],"oscillators,":[143],"regardless":[144],"form":[147],"energy.":[149],"derive":[151],"expressions":[152],"transient":[155],"steady-state":[157],"behavior":[158],"each":[160],"oscillator.":[161]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
