Integrating rotation from angular velocity
Abstract
The integration of the rotation from a given angular velocity is often required in practice. The present paper explores how the choice of the parametrization of rotation, when employed in conjuction with different numerical time-integration schemes, effects the accuracy and the computational efficiency. Three rotation parametrizations – the rotational vector, the Argyris tangential vector and the rotational quaternion – are combined with three different numerical time-integration schemes, including classical explicit Runge–Kutta method and the novel midpoint rule proposed here. The key result of the study is the assessment of the integration errors of various parametrization–integration method combinations. In order to assess the errors, we choose a time-dependent function corresponding to a rotational vector, and derive the related exact time-dependent angular velocity. This is then employed in the numerical solution as the data. The resulting numerically integrated approximate rotations are compared with the analytical solution. A novel global solution error norm for discrete solutions given by a set of values at chosen time-points is employed. Several characteristic angular velocity functions, resulting in small, finite and fast oscillating rotations are studied.
rotation
angular velocity
time integrations
quaternions
Runge-Kutta method
midpoint rule
rotacije
kotna hitrost
integracije po času
kvaternioni
metoda Runge-Kutta
metoda midpoint
true
false
false
Elsevier
Angleški jezik
Angleški jezik
Neznano
2015-07-10 10:12:48
2015-07-10 10:12:48
2021-04-21 12:27:30
0000-00-00 00:00:00
2011
0
0
Str. 723-733
št. 9
Letn. 42
sept. 2011
0000-00-00
NiDoloceno
NiDoloceno
NiDoloceno
624.07
0965-9978
10.1016/j.advengsoft.2011.05.010
5478497
34540032
http://drugg.fgg.uni-lj.si/3947/
1
https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=32188
P2011AES.pdf
P2011AES.pdf
1
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622931027993cd7d3ac3aeaed2d80c653451ff27ad51c0c3d897579f2726709c
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https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=85693
Fakulteta za gradbeništvo in geodezijo