Coordinate Transformations for Second-Order Systems: Part I General Transformations
SD Garvey (University of Nottingham), U Prells & MI Friswell (University of Wales Swansea)
Journal of Sound and Vibration, Vol. 258, No. 5, December 2002, pp. 885-909
When the dynamics of any general second order system are cast in a state-space format, the initial choice of the state-vector usually comprises one partition representing system displacements and another representing system velocities. Coordinate transformations can be defined which result in more general definitions of the state-vector. This paper discusses the general case of coordinate transformations of state-space representations for second order systems. It identifies one extremely important subset of such coordinate transformations – namely the set of structure-preserving transformations for second order systems – and it highlights the importance of these. It shows that one particular structure-preserving transformation results in a new system characterised by real diagonal matrices and presents a forceful case that this structure-preserving transformation should be considered to be the fundamental definition for the characteristic behaviour of general second order systems – in preference to the eigenvalue-eigenvector solutions conventionally accepted.
This material has been published in the Journal of Sound and Vibration, Vol. 258, No. 5, December 2002, pp. 885-909, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier Science.
Link to paper using doi:10.1006/jsvi.2002.5165
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