Premium
Comparison of solution strategies for multibody dynamics equations
Author(s) -
Mariti L.,
Belfiore N. P.,
Pennestrì E.,
Valentini P. P.
Publication year - 2011
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.3190
Subject(s) - rotation formalisms in three dimensions , orthogonalization , generalized coordinates , multibody system , moore–penrose pseudoinverse , constraint (computer aided design) , cartesian coordinate system , reduction (mathematics) , computer science , computation , basis (linear algebra) , log polar coordinates , mathematical optimization , algorithm , mathematics , inverse , mathematical analysis , geometry , physics , quantum mechanics
In the last decades, several different formalisms have been proposed in the literature in order to simulate the dynamics of multibody systems. First, the choice of the coordinates leads to very different formalisms. The set of constraint equations appears very different in complexity or in size depending on whether either relative , natural or reference point Cartesian coordinates are adopted. Second, once such a choice has been made, different solution strategies can be followed. It seems that formalisms based on redundant coordinates are often used in commercial software, whereas those based on a minimum number of coordinates are usually preferred in real‐time computations. In this paper, with reference to models with redundant absolute coordinates, the problem of coordinate reduction will be discussed and a group of 11 different methods will be compared on the basis of their computational efficiency. In particular, methods based on constraint orthogonalization and on the use of pseudoinverse matrices have been selected, together with other methods based on least‐squares block solution. The methods have been implemented on three different test cases. The main purpose is to provide hints and guidelines on the choice and availability of solution strategies during simulation of moderate size multibody systems. Copyright © 2011 John Wiley & Sons, Ltd.