{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:00:14Z","timestamp":1753887614412,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T00:00:00Z","timestamp":1575504000000},"content-version":"vor","delay-in-days":338,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","doi-asserted-by":"publisher","award":["18-21608S"],"award-info":[{"award-number":["18-21608S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The classic form of Hamilton\u2019s variational principle does not hold for circuits with dissipative elements. It is shown in the paper that this may not be true in the case of systems consisting of the so\u2010called higher\u2010order elements. Hamilton\u2019s principle is then extended to circuits containing the classical resistors and Frequency Dependent Negative Resistors (FDNRs). The extension is also made to any pair of elements which are the nearest neighbours on any <jats:italic>\u03a3<\/jats:italic>\u2010diagonal of Chua\u2019s table.<\/jats:p>","DOI":"10.1155\/2019\/2035324","type":"journal-article","created":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T23:30:35Z","timestamp":1575588635000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hamilton\u2019s Principle for Circuits with Dissipative Elements"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3055-4621","authenticated-orcid":false,"given":"Zden\u011bk","family":"Biolek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7607-6146","authenticated-orcid":false,"given":"Dalibor","family":"Biolek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2589-2722","authenticated-orcid":false,"given":"Viera","family":"Biolkov\u00e1","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,12,5]]},"reference":[{"volume-title":"The Variational Principles of Mechanics, Dover Books on Physics (Book 4)","year":"1986","author":"Lanczos C.","key":"e_1_2_10_1_2"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.53.1890"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.3034080"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcs.1980.1084742"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/tct.1971.1083337"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature06932"},{"key":"e_1_2_10_7_2","unstructured":"ChuaL. O. Memristors Proceedings of the 2nd Memristor and Memristive Systems Symposium November 2008 Berkeley CA USA University of California."},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/proc.1968.6599"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2002.803532"},{"key":"e_1_2_10_10_2","doi-asserted-by":"crossref","unstructured":"BiolekD. BiolekZ. Biolkov\u00e1V. andKolkaZ. Nonlinear inerter in the light of Chua\u2019s table of higher-order electrical elements Proceedings of IEEE Asia Pacific Conference on Circuits and Systems (APCCAS) October 2016 Jeju South Korea 617\u2013620 https:\/\/doi.org\/10.1109\/apccas.2016.7804046 2-s2.0-85011032539.","DOI":"10.1109\/APCCAS.2016.7804046"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.13164\/re.2017.0397"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-019-05218-9"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1155\/2018\/5719397"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/tcsi.2014.2364694"},{"key":"e_1_2_10_15_2","first-page":"235","volume-title":"Nachrichten von der Gesellschaft der Wissenschaften zu G\u00f6ttingen, Mathematisch-Physikalische Klasse","author":"Noether E.","year":"1918"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/2035324.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/2035324.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2019\/2035324","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T12:35:37Z","timestamp":1723034137000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2019\/2035324"}},"subtitle":[],"editor":[{"given":"Christos","family":"Volos","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1155\/2019\/2035324"],"URL":"https:\/\/doi.org\/10.1155\/2019\/2035324","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2019,1]]},"assertion":[{"value":"2019-08-12","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-10-08","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-12-05","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"2035324"}}