On the Poincar<mo063017.jpg> Map of the Almost-Periodic Oscillation of the Periodically Excited Li<mo063017.jpg>nard System

Tosiro KOGA; Masaharu SHINAGAWA

On the Poincar Map of the Almost-Periodic Oscillation of the Periodically Excited Linard System

Tosiro KOGA, Masaharu SHINAGAWA

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This paper clarifies some properties of the Poincar map of the almost periodic oscillation, which is generated by a periodically excited nonlinear system described by a Linard equation. Arguments in this paper are based on the extended Linard theorem already published by the present authors and are focused on the almost periodic oscillations which may occur in the Linard system under a certain constraint on the external force. As the main result, it is shown that the Poincar map of the almost periodic oscillation drawn on the Linard plane forms a simple closed continuous curve, under an explicitly given condition on the external force e (t) = A sin (ωt+θ), for arbitrary value of the amplitude A except for a set of the values ω with zero measure.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.6 pp.1401-1405

Publication Date: 1991/06/25

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Type of Manuscript: Special Section PAPER (Special Issue on Nonlinear Theory and Its Applications)

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Tosiro KOGA
Masaharu SHINAGAWA

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Tosiro KOGA, Masaharu SHINAGAWA, "On the Poincar Map of the Almost-Periodic Oscillation of the Periodically Excited Linard System" in IEICE TRANSACTIONS on Fundamentals, vol. E74-A, no. 6, pp. 1401-1405, June 1991, doi: .
Abstract: This paper clarifies some properties of the Poincar map of the almost periodic oscillation, which is generated by a periodically excited nonlinear system described by a Linard equation. Arguments in this paper are based on the extended Linard theorem already published by the present authors and are focused on the almost periodic oscillations which may occur in the Linard system under a certain constraint on the external force. As the main result, it is shown that the Poincar map of the almost periodic oscillation drawn on the Linard plane forms a simple closed continuous curve, under an explicitly given condition on the external force e (t) = A sin (ωt+θ), for arbitrary value of the amplitude A except for a set of the values ω with zero measure.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_6_1401/_p

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@ARTICLE{e74-a_6_1401,
author={Tosiro KOGA, Masaharu SHINAGAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Poincar Map of the Almost-Periodic Oscillation of the Periodically Excited Linard System},
year={1991},
volume={E74-A},
number={6},
pages={1401-1405},
abstract={This paper clarifies some properties of the Poincar map of the almost periodic oscillation, which is generated by a periodically excited nonlinear system described by a Linard equation. Arguments in this paper are based on the extended Linard theorem already published by the present authors and are focused on the almost periodic oscillations which may occur in the Linard system under a certain constraint on the external force. As the main result, it is shown that the Poincar map of the almost periodic oscillation drawn on the Linard plane forms a simple closed continuous curve, under an explicitly given condition on the external force e (t) = A sin (ωt+θ), for arbitrary value of the amplitude A except for a set of the values ω with zero measure.},
keywords={},
doi={},
ISSN={},
month={June},}

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TY - JOUR
TI - On the Poincar Map of the Almost-Periodic Oscillation of the Periodically Excited Linard System
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1401
EP - 1405
AU - Tosiro KOGA
AU - Masaharu SHINAGAWA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 1991
AB - This paper clarifies some properties of the Poincar map of the almost periodic oscillation, which is generated by a periodically excited nonlinear system described by a Linard equation. Arguments in this paper are based on the extended Linard theorem already published by the present authors and are focused on the almost periodic oscillations which may occur in the Linard system under a certain constraint on the external force. As the main result, it is shown that the Poincar map of the almost periodic oscillation drawn on the Linard plane forms a simple closed continuous curve, under an explicitly given condition on the external force e (t) = A sin (ωt+θ), for arbitrary value of the amplitude A except for a set of the values ω with zero measure.
ER -