Explicit Newmark/Verlet algorithm for time integration of the rotational dynamics of rigid bodies

We reformulate the traditional velocity based vector‐space Newmark algorithm for the rotational dynamics of rigid bodies, that is for the setting of the SO(3) Lie group. We show that the most naive re‐write of the vector space algorithm possesses the properties of symplecticity and (almost) momentum...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2005-04, Vol.62 (15), p.2154-2177
Main Authors: Krysl, P., Endres, L.
Format: Article
Language:English
Subjects:
3D rotation
explicit integrator
Newmark
rigid body dynamics
SO group
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Summary:We reformulate the traditional velocity based vector‐space Newmark algorithm for the rotational dynamics of rigid bodies, that is for the setting of the SO(3) Lie group. We show that the most naive re‐write of the vector space algorithm possesses the properties of symplecticity and (almost) momentum conservation. Thus, we obtain an explicit algorithm for rigid body dynamics that matches or exceeds performance of existing algorithms, but which curiously does not seem to have been considered in the open literature so far. Copyright © 2005 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.1272