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Critical study of Newmark-scheme on manifold of finite rotations

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Original languageEnglish
Pages (from-to)817-828
Number of pages12
JournalComputer Methods in Applied Mechanics and Engineering
Issue number8-10
Publication statusPublished - 21 Dec 2001
Publication typeA1 Journal article-refereed


In this paper, we show that the usual material form of the Newmark-time-stepping scheme of finite rotations is only a simplified version of the correct formula. This is because spin material rotation vectors, angular velocity vectors and angular accelerations vectors belong to different tangential vector spaces of a manifold at separate time moments. We give corrected Newmark-time-stepping schemes for material description and for spatial description. © 2001 Elsevier Science B.V. All rights reserved.

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