Subharmonic resonances of the parametrically driven pendulum

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Subharmonic resonances of the parametrically driven pendulum. / Butikov, Eugene I.

In: Journal of Physics A: Mathematical and General, Vol. 35, No. 30, 02.08.2002, p. 6209-6231.

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

Author

Butikov, Eugene I. / Subharmonic resonances of the parametrically driven pendulum. In: Journal of Physics A: Mathematical and General. 2002 ; Vol. 35, No. 30. pp. 6209-6231.

BibTeX

@article{c71e884f714946f18f56c3c2281ede5e,

title = "Subharmonic resonances of the parametrically driven pendulum",

abstract = "A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries of these modes in the parameter space are determined. New related modes of regular behaviour are described and explained. The conditions of the inverted pendulum stability are determined with greater precision than previous results. A computer program simulating the physical system supports the analytical investigation.",

author = "Butikov, {Eugene I.}",

year = "2002",

month = aug,

day = "2",

doi = "10.1088/0305-4470/35/30/301",

language = "English",

volume = "35",

pages = "6209--6231",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "30",

}

RIS

TY - JOUR

T1 - Subharmonic resonances of the parametrically driven pendulum

AU - Butikov, Eugene I.

PY - 2002/8/2

Y1 - 2002/8/2

N2 - A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries of these modes in the parameter space are determined. New related modes of regular behaviour are described and explained. The conditions of the inverted pendulum stability are determined with greater precision than previous results. A computer program simulating the physical system supports the analytical investigation.

AB - A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries of these modes in the parameter space are determined. New related modes of regular behaviour are described and explained. The conditions of the inverted pendulum stability are determined with greater precision than previous results. A computer program simulating the physical system supports the analytical investigation.

UR - http://www.scopus.com/inward/record.url?scp=0037008545&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/35/30/301

DO - 10.1088/0305-4470/35/30/301

M3 - Article

AN - SCOPUS:0037008545

VL - 35

SP - 6209

EP - 6231

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 30

ER -

ID: 51954575