Abstract
If the mass matrix M is singular no standard transformation to a first order system is possible. In fact, in this case we cannot prescribe some initial velocities and the phase-space will have dimension less than 2n. This will be even more so, if the damping matrix, too, is singular; then we could not prescribe even some initial positions. In order to treat such systems we must first separate away these ‘inactive’ degrees of freedom and then arrive at phase-space matrices which have smaller dimension but their structure will be essentially the same as in the regular case studied before. Now, out of M, C, K only K is supposed to be positive definite while M, C are positive semidefinite.
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© 2011 Springer-Verlag Berlin Heidelberg
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Veselić, K. (2011). The Singular Mass Case. In: Damped Oscillations of Linear Systems. Lecture Notes in Mathematics(), vol 2023. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21335-9_4
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DOI: https://doi.org/10.1007/978-3-642-21335-9_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21334-2
Online ISBN: 978-3-642-21335-9
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