Full metadata
Title
Stability and reducibility of quasi-periodic systems
Description
In this work, we focused on the stability and reducibility of quasi-periodic systems. We examined the quasi-periodic linear Mathieu equation of the form x ̈+(ä+ϵ[cost+cosùt])x=0 The stability of solutions of Mathieu's equation as a function of parameter values (ä,ϵ) had been analyzed in this work. We used the Floquet type theory to generate stability diagrams which were used to determine the bounded regions of stability in the ä-ù plane for fixed ϵ. In the case of reducibility, we first applied the Lyapunov- Floquet (LF) transformation and modal transformation, which converted the linear part of the system into the Jordan form. Very importantly, quasi-periodic near-identity transformation was applied to reduce the system equations to a constant coefficient system by solving homological equations via harmonic balance. In this process we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system to a constant one.
Date Created
2012
Contributors
- Ezekiel, Evi (Author)
- Redkar, Sangram (Thesis advisor)
- Meitz, Robert (Committee member)
- Nam, Changho (Committee member)
- Arizona State University (Publisher)
Topical Subject
Resource Type
Extent
vii, 56 p. : ill. (some col.)
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.I.15103
Statement of Responsibility
by Evi Ezekiel
Description Source
Viewed on June 3, 2013
Level of coding
full
Note
thesis
Partial requirement for: M.S.Tech, Arizona State University, 2012
bibliography
Includes bibliographical references (p. 54-56)
Field of study: Mechanical engineering
System Created
- 2012-08-24 06:29:44
System Modified
- 2021-08-30 01:45:38
- 3 years 2 months ago
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