Quaternion-based rigid body rotation integration algorithms for use in particle methods

The resolution of translational motion in discrete element method and molecular dynamics applications is a straightforward task; however, resolving rotational motion is less obvious. Many applications update rotation using an explicit integration involving products of matrices, which has well‐known...

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Vydané v:	International journal for numerical methods in engineering Ročník 74; číslo 8; s. 1303 - 1313
Hlavní autori:	Johnson, Scott M., Williams, John R., Cook, Benjamin K.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Chichester, UK John Wiley & Sons, Ltd 21.05.2008 Wiley
Predmet:	Computational techniques DEM dynamics Exact sciences and technology Fundamental areas of phenomenology (including applications) integration Mathematical methods in physics motion numerical methods Physics rigid body rotation Solid dynamics (ballistics, collision, multibody system, stabilization...) Solid mechanics Rigid bodies numerical methods Numerical integration motion Quaternion Molecular dynamics method rotation Solid dynamic Step method Taylor series Discrete element method Orthogonality Modeling DEM Rotating system Particle method dynamics rigid body Meshless method Series expansion integration Rotation angle
ISSN:	0029-5981, 1097-0207
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Popis
Shrnutí:	The resolution of translational motion in discrete element method and molecular dynamics applications is a straightforward task; however, resolving rotational motion is less obvious. Many applications update rotation using an explicit integration involving products of matrices, which has well‐known drawbacks. Although rigid body rotation has received attention in large‐angle rotation applications, relatively little attention has been dedicated to the unique requirements of particle methods using explicit time‐stepping algorithms. This paper reviews existing explicit algorithms and shows the benefits of using a quaternion‐based re‐parameterization of both the central difference algorithm and the approach of Munjiza et al. (Int. J. Numer. Meth. Engng 2003; 56:36–55). The improvement not only provides guaranteed orthonormality of the resulting rotation but also allows the assumption of small‐angle rotation to be relaxed and the use of a more accurate Taylor expansion instead. The current and quaternion‐based algorithms are compared for accuracy and computational efficiency. Copyright © 2007 John Wiley & Sons, Ltd.
Bibliografia:	istex:2FE5924930D5E05D1E3A9E5708BCF855414D7C08 ark:/67375/WNG-SK907247-D United States Department of Energy's National Nuclear Security Administration; - No. DE-AC04-94AL85000 ArticleID:NME2210 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0029-5981 1097-0207
DOI:	10.1002/nme.2210