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Numerical integration of rigid body dynamics in terms of quaternions
Author(s) -
Siebert Ralf,
Betsch Peter
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810139
Subject(s) - quaternion , parametrization (atmospheric modeling) , rigid body dynamics , rigid body , mathematics , equations of motion , unit (ring theory) , euler's formula , algebraic number , euler equations , mathematical analysis , classical mechanics , physics , geometry , mathematics education , quantum mechanics , radiative transfer
Unit–quaternions (or Euler parameter) are known to be well–suited for the singularity–free parametrization of finite rotations. Despite of this advantage, unit quaternions were rarely used to formulate the equations of motion (exceptions are the works by Nikravesh [1] and Haug [2]). This might be related to the fact, that the unit–quaternions are redundant, which requires the use of algebraic constraints in the equations of motion. Nowadays robust energy consistent integrators are available for the numerical solution of these differential–algebraic equations (DAEs). In the present work a mechanical integrator for the quaternions will be derived. This will be done by a size–reduction from the director formulation of the equations of motion, which also has the form of DAEs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)