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Simple and efficient integration of rigid rotations suitable for constraint solvers
Author(s) -
Koziara Tomasz,
Bićanić Nenad
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2711
Subject(s) - simple (philosophy) , scheme (mathematics) , scope (computer science) , constraint (computer aided design) , mathematical optimization , computer science , stability (learning theory) , term (time) , algorithm , algebraic number , mathematics , geometry , mathematical analysis , philosophy , physics , epistemology , quantum mechanics , machine learning , programming language
Simple and efficient way of integrating rigid rotations is presented. The algorithm is stable, second‐order accurate, and in its explicit version involves evaluation of only two exponential maps per time step. The semi‐explicit version of the proposed scheme improves upon the long‐term stability, while it retains the explicitness in the force evaluation. The algebraic structure of both schemes makes them suitable forthe analysis of constrained multi‐body systems. The explicit algorithm is specifically aimed at the analysis involving small incremental rotations, where its modest computational cost becomes the major advantage. The semi‐explicit scheme naturally broadens the scope of possible applications. Copyright © 2009 John Wiley & Sons, Ltd.