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Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation. / Butikov, Eugene I.

в: American Journal of Physics, Том 86, № 4, 01.04.2018, стр. 257-267.

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Butikov, Eugene I. / Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation. в: American Journal of Physics. 2018 ; Том 86, № 4. стр. 257-267.

BibTeX

@article{1c7c5ed08ac84134853f3db5b7920609,
title = "Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation",
abstract = "Simple analytical expressions are suggested for transition curves that separate, in the Ince-Strutt diagram, different types of solutions to the famous Mathieu equation. The derivations of these expressions in this paper rely on physically meaningful periodic solutions describing various regular motions of a familiar nonlinear mechanical system - a rigid planar pendulum with a vertically oscillating pivot. The paper is accompanied by a relevant simulation program.",
keywords = "INVERTED PENDULUM",
author = "Butikov, {Eugene I.}",
year = "2018",
month = apr,
day = "1",
doi = "10.1119/1.5021895",
language = "English",
volume = "86",
pages = "257--267",
journal = "American Journal of Physics",
issn = "0002-9505",
publisher = "American Association of Physics Teachers",
number = "4",

}

RIS

TY - JOUR

T1 - Analytical expressions for stability regions in the Ince-Strutt diagram of Mathieu equation

AU - Butikov, Eugene I.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - Simple analytical expressions are suggested for transition curves that separate, in the Ince-Strutt diagram, different types of solutions to the famous Mathieu equation. The derivations of these expressions in this paper rely on physically meaningful periodic solutions describing various regular motions of a familiar nonlinear mechanical system - a rigid planar pendulum with a vertically oscillating pivot. The paper is accompanied by a relevant simulation program.

AB - Simple analytical expressions are suggested for transition curves that separate, in the Ince-Strutt diagram, different types of solutions to the famous Mathieu equation. The derivations of these expressions in this paper rely on physically meaningful periodic solutions describing various regular motions of a familiar nonlinear mechanical system - a rigid planar pendulum with a vertically oscillating pivot. The paper is accompanied by a relevant simulation program.

KW - INVERTED PENDULUM

UR - http://www.scopus.com/inward/record.url?scp=85044330630&partnerID=8YFLogxK

U2 - 10.1119/1.5021895

DO - 10.1119/1.5021895

M3 - Article

AN - SCOPUS:85044330630

VL - 86

SP - 257

EP - 267

JO - American Journal of Physics

JF - American Journal of Physics

SN - 0002-9505

IS - 4

ER -

ID: 33148644