Dynamics of the pendulum with periodically varying length

被引：60

作者：

Belyakov, Anton O. ^{[1
]}

Seyranian, Alexander P. ^{[1
]}

Luongo, Angelo ^{[2
]}

机构：

[1] Moscow MV Lomonosov State Univ, Inst Mech, Moscow 119192, Russia

[2] Univ Aquila, DISAT, I-67040 Laquila, Italy

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2009年 / 238卷 / 16期

关键词：

Pendulum of variable length; Regular rotation; Tumbling chaos; Averaging method; Stability of limit cycle; Quasi-linear oscillatory system; STABILITY;

D O I：

10.1016/j.physd.2009.04.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Dynamic behavior of a weightless rod with a point mass sliding along the rod axis according to periodic law is studied. This is the pendulum with periodically varying length which is also treated as a simple model of a child's swing. Asymptotic expressions for boundaries of instability domains near resonance frequencies are derived. Domains for oscillation, rotation, and oscillation-rotation motions in parameter space are found analytically and compared with a numerical Study. Chaotic motions of the pendulum depending on problem parameters are investigated numerically. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：1589 / 1597

页数：9

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