Premium
On the asymptotics for solutions of system of two linear oscillators with slowly decreasing coupling
Author(s) -
Nesterov P.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800179
Subject(s) - coupling (piping) , mathematics , term (time) , construct (python library) , mathematical analysis , linear system , physics , quantum mechanics , computer science , engineering , programming language , mechanical engineering
In this paper, we construct the asymptotic formulas for solutions of system of two linear oscillators with slowly decreasing coupling as t → ∞. To study this system we use the specially developed variant of the method of averaging that was introduced for investigation of systems with oscillatory decreasing coefficients. To get the asymptotics for the solutions we involve Levinson's fundamental theorem. Moreover, we estimate the o(1) term in asymptotic formulas.