Browse > Article
http://dx.doi.org/10.4134/CKMS.2003.18.4.755

ON SOME SPECIAL CONDITIONS OF n-TH ORDER NON-OSCILLATORY NONLINEAR SYSTEMS  

Alam, M.-Shamsul (Department of Mathematics Bangladesh Institute of Technology)
Hossain, M.B. (Department of Mathematics Bangladesh Institute of Technology)
Publication Information
Communications of the Korean Mathematical Society / v.18, no.4, 2003 , pp. 755-765 More about this Journal
Abstract
Krylov-Bogoliubov-Mitropolskii method has been extended to obtain asymptotic solution of n-th order nonlinear differential system characterized by certain non-oscillatory processes. The damping force is considered in such a manner that one of the characteristic roots of the linear system becomes small and others are in integral multiple. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical method.
Keywords
asymptotic expansion; non-oscillation; over-damped systems;
Citations & Related Records
연도 인용수 순위
  • Reference
1 An asymptotic method for second-order critically damped nonlinear equations /
[ M.A.Sattar ] / J. Franklin Inst.   DOI   ScienceOn
2 An asymptotic method for three-dimensional over-damped nonlinear systems /
[ M.A.Sattar ] / Ganit(J. Bangladesh Math. Soc.)
3 On some special conditions of n-th order over-damped nonlinear systems /
[ M.Shamsul Alam ] / Bull. Calcutta Math.Soc.
4 Vibration of a viscoelastic rod with small nonlinearities /
[ R.W.Lardner;G.N.Bojadziev ] / Meccanica   DOI   ScienceOn
5 /
[ N.N.Krylov;N.N.Bogoliubov ] / Introduction to Nonlinear Mechanics
6 On some special conditions of third-order over-damped nonlinear systems /
[ M.Shamsul Alam ] / Indian J. Pure Appl. Math.
7 Asymptotic methods for second-order over-damped and critically damped nonlinear systems /
[ M.Shamsul Alam ] / Soochow Journal of Math.
8 /
[ N.N.Bogoliubov;Yu.A.Mitropolskii ] / Asymptotic Methods in the Theory of Nonlinear Oscillations
9 Damped nonlinear oscillations modeled by a 3-dimensional differential system /
[ G.N.Bojadziev ] / Acta Mech.   DOI
10 Longitudinal, torsional and bending vibrations of a uniform bar with nonlinear internal friction and relaxation /
[ Z.Osiniskii ] / Nonlinear Vibration Problems
11 On asymptotic method of Krylov-Bogoliubov for over-damped nonlinear systems /
[ I.S.N.Murty;B.L.Deekshatulu;G.Krisna ] / J. Franklin Inst.   DOI   ScienceOn
12 Method of variation of parameters for over-damped nonlinear systems /
[ I.S.N.Murty;B.L.Deekshatulu ] / J. Control   DOI
13 A unified Krylov-Bogoliubov-Mitroplskii method for solving n-th order nonlinear systems /
[ M.Shamsul Alam ] / J. Franklin Inst.   DOI   ScienceOn