Uniform asymptotic stability of time-varying damped harmonic oscillators
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- by Kazuki Ishihara and Jitsuro Sugie HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 4 (2017), 31-46
Abstract:
This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator \begin{equation*} x” + h(t)\!\:x’ + \omega ^2x = 0 \end{equation*} is uniformly asymptotically stable, where $h\!: [0,\infty ) \to [0,\infty )$ is locally integrable. These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient $h$. The obtained sufficient conditions are compared with known conditions for uniform asymptotic stability. Two diagrams are included to facilitate understanding of the conditions. By giving a concrete example, remaining problems are pointed out.References
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Additional Information
- Kazuki Ishihara
- Affiliation: Department of Mathematics, Shimane University, Matsue 690-8504, Japan
- Email: kazu2520asyst@gmail.com
- Jitsuro Sugie
- Affiliation: Department of Mathematics, Shimane University, Matsue 690-8504, Japan
- MR Author ID: 168705
- Email: jsugie@riko.shimane-u.ac.jp
- Received by editor(s): February 24, 2017
- Received by editor(s) in revised form: April 22, 2017, and June 16, 2017
- Published electronically: October 13, 2017
- Additional Notes: The second author’s work was supported in part by Grant-in-Aid for Scientific Research No. 17K05327 from the Japan Society for the Promotion of Science.
The authors would like to thank an anonymous referee for reading carefully and giving valuable comments. - Communicated by: Wenxian Shen
- © Copyright 2017 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 4 (2017), 31-46
- MSC (2010): Primary 34D20, 34D45; Secondary 37C70, 93D20
- DOI: https://doi.org/10.1090/bproc/30
- MathSciNet review: 3746977