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Reduction of second order linear dynamical systems, with large dissipation, by state variable transformations

Published online by Cambridge University Press:  17 February 2009

R. B. Leipnik
R. B. Leipnik
Affiliation:
Department of Mathematics, University of California, Santa Barbara, U.S.A.
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Abstract

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Linear dynamical systems of the Rayleigh form are transformed by linear state variable transformations , where A and B are chosen to simplify analysis and reduce computing time. In particular, A is essentially a square root of M, and B is a Lyapunov quotient of C by A. Neither K nor C is required to be symmetric, nor is C small. The resulting state-space systems are analysed by factorisation of the evolution matrices into reducible factors. Eigenvectors and eigenvalues are determined by these factors. Conditions for further simplification are derived in terms of Kronecker determinants. These results are compared with classical reductions of Rayleigh, Duncan, and Caughey, which are reviewed at the outset.

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 2 , October 1990 , pp. 207 - 222
Copyright
Copyright © Australian Mathematical Society 1990

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