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The Floquet stability of systems of differential equations with piecewise constant periodic coefficients is considered. In the "two-step" case the monodromy matrix is the product of two matrix exponentials. It can be evaluated either by reducing the matrix exponentials to polynomials on the eigenvalues of the corresponding matrices or, without knowledge of the eigenvalues, by using the Baker�Campbell�Hausdorff formula. The two methods are discussed and applied to several examples including the "two-step" dissipative Hill's equation introduced recently H. Tasso, G.N. Throumoulopoulos [Phys. Plasmas 9 (2002) 2662] to stabilize the "resistive wall mode" in magnetically confined plasmas. Application to large systems and matrices is not only possible but also needed for the full understanding of the dynamic stabilization of the resistive wall mode. Its practical implementation is discussed.

This paper was presented at the 44th Annual Meeting of the Division of Plasma Physics of the American Physical Society, 11-15 November 2002, Orlando, FL, USA.

Additional information

Authors: TASSO H, Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching (DE);THROUMOULOPOULOS G N, Association Euratom-Hellenic Republic, University of Ioannina, Department of Physics, Section of Theoretical Physics, Ioannina (GR)
Bibliographic Reference: An article published in: Physics Letters A, Volume 307, Issues 5-6 , 10 February (2003), pp.304-312
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Record Number: 200316029 / Last updated on: 2003-03-07
Original language: en
Available languages: en