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Application of Bloch Analysis to the Stability Investigation of Hamiltonian Systems of Linear Differential Equations with Periodic Coefficients
Author(s) -
Stoffel A.
Publication year - 1990
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.19900700303
Subject(s) - eigenvalues and eigenvectors , mathematics , mathematical analysis , differential equation , stability (learning theory) , hamiltonian system , hamiltonian (control theory) , instability , operator (biology) , physics , quantum mechanics , mathematical optimization , biochemistry , chemistry , repressor , machine learning , computer science , transcription factor , gene
Abstract The direct integral decomposition of the self‐adjoint operator associated with the differential equation is used to determine the set of parameters for which the equilibrium solution is stable. For systems with more than one degree of freedom even parameters in the interior of the spectrum may give rise to instability. The possibility of approximation of the eigenvalues without numerical solution of the differential equation, the qualitative behaviour considering small perturbations and the relation to Krein's stability theory are outlined. The described method is applied to models of two‐bladed wind turbines.