CO-ORDINATE TRANSFORMATIONS FOR SECOND ORDER SYSTEMS. PART I: GENERAL TRANSFORMATIONS

✍ Scribed by S.D. GARVEY; M.I. FRISWELL; U. PRELLS

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 283 KB
• Volume: 258
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2002.5165

✦ Synopsis

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. Co-ordinate transformations can be defined which result in more general definitions of the state vector. This paper discusses the general case of co-ordinate 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 structurepreserving transformation results in a new system characterized 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.