An Implicit Transition Matrix Approach to Stability Analysis of Flexible Multi-Body Systems

The stability of linear systems defined by ordinarydifferential equations with constant or periodic coefficients can beassessed from the spectral radius of their transition matrix. Inclassical applications of this theory, the transition matrix isexplicitly computed first, then its eigenvalues are evaluated; if thelargest eigenvalue is larger than unity, the system is unstable. Theproposed implicit transition matrix approach extracts the dominanteigenvalues of the transition matrix using the Arnoldi algorithm,without the explicit computation of this matrix. As a result, theproposed implicit method yields stability information at a far lowercomputational cost than that of the classical approach, and is ideallysuited for stability computations of systems involving a large number ofdegrees of freedom. Examples of application of the proposed methodologyto flexible multi-body systems are presented that demonstrate itsaccuracy and computational efficiency.

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