Publication result detail

Lagrangian for circuits with higher-order elements

BIOLEK, Z.; BIOLEK, D.; BIOLKOVÁ, V.

Original Title

Lagrangian for circuits with higher-order elements

English Title

Lagrangian for circuits with higher-order elements

Type

WoS Article

Original Abstract

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.

English abstract

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.

Keywords

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

Key words in English

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

Authors

BIOLEK, Z.; BIOLEK, D.; BIOLKOVÁ, V.

RIV year

2020

Released

29.10.2019

Publisher

MDPI

Location

Basel, Switzerland

ISBN

1099-4300

Periodical

Entropy

Volume

21

Number

11

State

Swiss Confederation

Pages from

1

Pages to

19

Pages count

19

URL

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

Full text in the Digital Library

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",
  url="https://www.mdpi.com/1099-4300/21/11/1059"
}

Documents

entropy-21-01059