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

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

In: American Journal of Physics, Vol. 86, No. 4, 01.04.2018, p. 257-267.

Research output: Contribution to journal › Article › peer-review

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