The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters
Joint Authors
Source
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-08-31
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Let a(t),b(t) be continuous T-periodic functions with ∫0Tb(t)dt=0.
We establish one stability criterion for the linear damped oscillator x′′+b(t)x′+a(t)x=0.
Moreover, based on the computation of the corresponding Birkhoff normal forms, we present a sufficient condition for the stability of the equilibrium of the nonlinear damped oscillator x′′+b(t)x′+a(t)x+c(t)x2n-1+e(t,x)=0, where n≥2,c(t) is a continuous T-periodic function, e(t,x) is continuous T-periodic in t and dominated by the power x2n in a neighborhood of x=0.
American Psychological Association (APA)
Chu, Jifeng& Xia, Ting. 2010. The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters. Abstract and Applied Analysis،Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-460436
Modern Language Association (MLA)
Chu, Jifeng& Xia, Ting. The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters. Abstract and Applied Analysis No. 2010 (2010), pp.1-12.
https://search.emarefa.net/detail/BIM-460436
American Medical Association (AMA)
Chu, Jifeng& Xia, Ting. The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters. Abstract and Applied Analysis. 2010. Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-460436
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460436