Detail publikace

Lagrangian for circuits with higher-order elements

BIOLEK, Z. BIOLEK, D. BIOLKOVÁ, V.

Originální název

Lagrangian for circuits with higher-order elements

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

The 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.

Klíčová slova

Hamilton’s variational principle; higher-order element; memristor; Lagrangian; Chua’s table; Euler-Lagrange equation

Autoři

BIOLEK, Z.; BIOLEK, D.; BIOLKOVÁ, V.

Vydáno

29. 10. 2019

Nakladatel

MDPI

Místo

Basel, Switzerland

ISSN

1099-4300

Periodikum

ENTROPY

Ročník

21

Číslo

11

Stát

Švýcarská konfederace

Strany od

1

Strany do

19

Strany počet

19

URL

https://www.mdpi.com/1099-4300/21/11/1059

Plný text v Digitální knihovně

http://hdl.handle.net/11012/180820

BibTex

@article{BUT159543,
  author="Zdeněk {Biolek} and Dalibor {Biolek} and Viera {Biolková}",
  title="Lagrangian for circuits with higher-order elements",
  journal="ENTROPY",
  year="2019",
  volume="21",
  number="11",
  pages="1--19",
  doi="10.3390/e21111059",
  issn="1099-4300",
  url="https://www.mdpi.com/1099-4300/21/11/1059"
}