{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T17:11:39Z","timestamp":1774372299405,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/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":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The necessary and sufficient conditions of the validity of Hamilton\u2019s variational principle for circuits consisting of (\u03b1,\u03b2) elements from Chua\u2019s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called \u03a3-diagonal with a constant sum of the indices \u03b1 and \u03b2. In this case, the Lagrangian is the sum of the state functions of the elements of the L or +R types minus the sum of the state functions of the elements of the C or \u2212R types. The equations of motion generated by this Lagrangian are always of even-order. If all the elements are linear, the equations of motion contain only even-order derivatives of the independent variable. Conclusions are illustrated on an example of the synthesis of the Pais\u2013Uhlenbeck oscillator via the elements from Chua\u2019s table.<\/jats:p>","DOI":"10.3390\/e21111059","type":"journal-article","created":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T05:18:26Z","timestamp":1572499106000},"page":"1059","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Lagrangian for Circuits with Higher-Order Elements"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3055-4621","authenticated-orcid":false,"given":"Zdenek","family":"Biolek","sequence":"first","affiliation":[{"name":"Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech Republic"},{"name":"Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7607-6146","authenticated-orcid":false,"given":"Dalibor","family":"Biolek","sequence":"additional","affiliation":[{"name":"Department of Microelectronics, Brno University of Technology, 616 00 Brno, Czech Republic"},{"name":"Department of Electrical Engineering, University of Defence, 662 10 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2589-2722","authenticated-orcid":false,"given":"Viera","family":"Biolkova","sequence":"additional","affiliation":[{"name":"Department of Radio Electronics, Brno University of Technology, 616 00 Brno, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,29]]},"reference":[{"key":"ref_1","unstructured":"Lanczos, C. 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