Lagrangian for circuits with higher-order elements

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dc.contributor.authorBiolek, Zdeněkcs
dc.contributor.authorBiolek, Daliborcs
dc.contributor.authorBiolková, Vieracs
dc.coverage.issue11cs
dc.coverage.volume21cs
dc.date.issued2019-10-29cs
dc.description.abstractThe necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (alpha,beta) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called -diagonal with a constant sum of the indices alpha and beta. In this case, the Lagrangian is the sum of the state functions of elements of the L or +R types minus the sum of the state functions of elements of the C or -R types. The equations of motion generated by this Lagrangian are always of even-order. If all 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-Uhlenbeck oscillator via the elements from Chua’s table.en
dc.formattextcs
dc.format.extent1-19cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationENTROPY. 2019, vol. 21, issue 11, p. 1-19.en
dc.identifier.doi10.3390/e21111059cs
dc.identifier.issn1099-4300cs
dc.identifier.orcid0000-0002-7607-6146cs
dc.identifier.orcid0000-0003-2589-2722cs
dc.identifier.other159543cs
dc.identifier.researcheridE-4125-2018cs
dc.identifier.researcheridE-3698-2018cs
dc.identifier.scopus6603672687cs
dc.identifier.scopus6506028849cs
dc.identifier.urihttp://hdl.handle.net/11012/180820
dc.language.isoencs
dc.publisherMDPIcs
dc.relation.ispartofENTROPYcs
dc.relation.urihttps://www.mdpi.com/1099-4300/21/11/1059cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1099-4300/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectHamilton’s variational principleen
dc.subjecthigher-order elementen
dc.subjectmemristoren
dc.subjectLagrangianen
dc.subjectChua’s tableen
dc.subjectEuler-Lagrange equationen
dc.titleLagrangian for circuits with higher-order elementsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-159543en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:39:00en
sync.item.modts2025.01.17 16:33:56en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav radioelektronikycs
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav mikroelektronikycs
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Centrum senzorických, informačních a komunikačních systémůcs
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