Remote Access Proceedings of the American Mathematical Society Series B
Gold Open Access

Proceedings of the American Mathematical Society Series B

ISSN 2330-1511

   
 
 

 

Uniform asymptotic stability of time-varying damped harmonic oscillators


Authors: Kazuki Ishihara and Jitsuro Sugie
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
Published electronically: October 13, 2017
MathSciNet review: 3746977
Full-text PDF Open Access
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society, Series B with MSC (2010): 34D20, 34D45, 37C70, 93D20

Retrieve articles in all journals with MSC (2010): 34D20, 34D45, 37C70, 93D20


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

Keywords: Uniform asymptotic stability, damped linear oscillator, growth condition
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
Article copyright: © Copyright 2017 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)