Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended and applied to certain over-damped nonlinear system in which the linear equation has two almost equal roots. The method is illustrated by an example.
| Published in | Pure and Applied Mathematics Journal (Volume 2, Issue 2) |
| DOI | 10.11648/j.pamj.20130202.18 |
| Page(s) | 101-105 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Nonlinear System, Unperturbed Equation, Over-Damped Oscillatory System, Equal Roots
| [1] | N.N, Krylov and N.N., Bogoliubov, Introduction to Nonli-near Mechanics. Princeton University Press, New Jersey, 1947. |
| [2] | N. N, Bogoliubov and Yu. Mitropolskii, Asymptotic Me-thods in the Theory of nonlinear Oscillations, Gordan and Breach, New York, 1961. |
| [3] | Yu.,Mitropolskii, "Problems on Asymptotic Methods of Non-stationary Oscillations" (in Russian), Izdat, Nauka, Moscow, 1964.P. Popov, "A generalization of the Bogoli-ubov asymptotic method in the theory of nonlinear oscilla-tions", Dokl.Akad. Nauk SSSR 111, 1956, 308-310 (in Russian). |
| [4] | S. N. Murty, B. L. Deekshatulu and G. Krisna, "General asymptotic method of Krylov-Bogoliubov for over-damped nonlinear system", J. Frank Inst. 288 (1969), 49-46. |
| [5] | M.,Shamsul Alam, "A unified Krylov-Bogoliubov-Mitropolskii method for solving nth order nonlinear sys-tems", Journal of the Franklin Institute 339, 239-248, 2002. |
| [6] | M.,Shamsul Alam., "Asymptotic methods for second-order over-damped and critically damped nonlinear system", Soochow J. Math, 27, 187-200, 2001 . |
| [7] | Pinakee Dey, M. Zulfikar Ali, M. Shamsul Alam, An Asymptotic Method for Time Dependent Non-linear Over-damped Systems, J. Bangladesh Academy of sciences., Vol. 31, pp. 103-108, 2007. |
| [8] | Pinakee Dey, Method of Solution to the Over-Damped Nonlinear Vibrating System with Slowly Varying Coeffi-cients under Some Conditions, J. Mech. Cont. & Math. Sci. Vol -8 No-1, July, 2013. |
| [9] | H. Nayfeh, Introduction to perturbation Techniques, J. Wiley, New York, 1981. |
APA Style
Pinakee Dey. (2013). Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems. Pure and Applied Mathematics Journal, 2(2), 101-105. https://doi.org/10.11648/j.pamj.20130202.18
ACS Style
Pinakee Dey. Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems. Pure Appl. Math. J. 2013, 2(2), 101-105. doi: 10.11648/j.pamj.20130202.18
AMA Style
Pinakee Dey. Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems. Pure Appl Math J. 2013;2(2):101-105. doi: 10.11648/j.pamj.20130202.18
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Download@article{10.11648/j.pamj.20130202.18,
author = {Pinakee Dey},
title = {Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems},
journal = {Pure and Applied Mathematics Journal},
volume = {2},
number = {2},
pages = {101-105},
doi = {10.11648/j.pamj.20130202.18},
url = {https://doi.org/10.11648/j.pamj.20130202.18},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130202.18},
abstract = {Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended and applied to certain over-damped nonlinear system in which the linear equation has two almost equal roots. The method is illustrated by an example.},
year = {2013}
}
TY - JOUR T1 - Asymptotic Method for Certain over-Damped Nonlinear Vibrating Systems AU - Pinakee Dey Y1 - 2013/05/20 PY - 2013 N1 - https://doi.org/10.11648/j.pamj.20130202.18 DO - 10.11648/j.pamj.20130202.18 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 101 EP - 105 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20130202.18 AB - Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended and applied to certain over-damped nonlinear system in which the linear equation has two almost equal roots. The method is illustrated by an example. VL - 2 IS - 2 ER -
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