Analytical and Numerical Study on a Parametric Pendulum with the Step-Wave Modulation of Length and Forcing

A parametric pendulum excited by a discrete wave-modulated step function of length is subjected to a mathematical analysis and numerical modeling. We observe an existence of almost periodic solutions of ordinary differential equations with linear boundary value conditions. An exemplary oscillator su...

Full description

Saved in:
Bibliographic Details
Published inInternational journal of structural stability and dynamics Vol. 19; no. 5; p. 1941006
Main Authors Olejnik, Paweł, Fečkan, Michal, Awrejcewicz, Jan
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 01.05.2019
World Scientific Publishing Co. Pte., Ltd
Subjects
Differential equations
Elongation
Mathematical models
Ordinary differential equations
Pendulums
Step functions
Synchronism
piece-wise continuous system
quasi-periodic solutions
Variable length pendulum
step-wave modulation
forced oscillator
Online AccessGet full text
ISSN0219-4554
1793-6764
DOI10.1142/S0219455419410062

Cover

More Information
Summary:A parametric pendulum excited by a discrete wave-modulated step function of length is subjected to a mathematical analysis and numerical modeling. We observe an existence of almost periodic solutions of ordinary differential equations with linear boundary value conditions. An exemplary oscillator subject to both an almost periodic step elongation and forcing synchronizes with the forcing, tending to almost periodic motions like stable limit cycles. Conditions for that synchronization as well as trajectories of numerical solutions on time history plots and phase planes are shown to confirm correctness of the analytical derivations and dedicated numerical modeling.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0219-4554
1793-6764
DOI:10.1142/S0219455419410062