Ahmadian, Mehdi; Chou, Shui-Hang A new method for finding symmetric form of asymmetric finite-dimensional dynamic systems. (English) Zbl 0629.70020 J. Appl. Mech. 54, 700-705 (1987). A subclass of general lumped-parameter dynamic systems which can be transformed into an equivalent symmetric form is considered here. For the purpose of the present study, these systems are divided into two categories: those without velocity dependent forces (pseudo-conservative systems) and those with velocity dependent forces (pseudo-symmetric systems). For each category, the results on symmetrizability of matrices are used to develop an effective, systematic technique for computing the coordinate system in which the system is symmetric. The primary advantages of the technique presented in this study are twofold. First, it is computationally efficient and stable. Second, it can effectively handle systems with many degrees-of-freedom, unlike the trial and error approach suggested in previous studies [e.g. the first author and D. J. Inman, ibid. 53, 10-14 (1986; Zbl 0595.70022)]. Cited in 1 Document MSC: 70Q05 Control of mechanical systems 70F10 \(n\)-body problems 37-XX Dynamical systems and ergodic theory 93C15 Control/observation systems governed by ordinary differential equations Keywords:general lumped-parameter dynamic systems; pseudo-conservative systems; pseudo-symmetric systems; symmetrizability of matrices; trial and error approach Citations:Zbl 0595.70022 PDFBibTeX XMLCite \textit{M. Ahmadian} and \textit{S.-H. Chou}, J. Appl. Mech. 54, 700--705 (1987; Zbl 0629.70020) Full Text: DOI