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Preprints of the Keldysh Institute of Applied Mathematics, 1997, 043
(Mi ipmp1431)
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Resonances of Linear Differential Equations with Piecewise Constant Coefficients
Yu. F. Golubev
Abstract:
This paper develops a method to study and control parametric resonance in systems, which are governed by linear differential equations of the second order with periodic coefficients. This method allows finding a monodromy matrix as a result of composition of elementary phase flux transformations. The method is based on piecewise constant approximation of coefficients of the equations. A criterion for parametric resonance is found which is taking into account multiplicity of roots of the characteristic equation of monodromy and action of a dissipative forces as well. Complete study of parametric resonance is presented for Hill's equation and for equation of Mathieu's type in a special case of periodic two-step piecewise constant functions. For a case of a dissipative force the range of parameters for resonance to occur is shown as well.
Citation:
Yu. F. Golubev, “Resonances of Linear Differential Equations with Piecewise Constant Coefficients”, Keldysh Institute preprints, 1997, 043
Linking options:
https://www.mathnet.ru/eng/ipmp1431 https://www.mathnet.ru/eng/ipmp/y1997/p43
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Statistics & downloads: |
Abstract page: | 161 | Full-text PDF : | 22 |
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