Integrating rotation from angular velocity

Abstract

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.

Keywords

rotacije;kotna hitrost;integracije po času;kvaternioni;metoda Runge-Kutta;metoda midpoint;rotation;angular velocity;time integrations;quaternions;Runge-Kutta method;midpoint rule;

Data

Language:	English
Year of publishing:	2011
Typology:	1.01 - Original Scientific Article
Organization:	UL FGG - Faculty of Civil and Geodetic Engineering
Publisher:	Elsevier
UDC:	624.07
COBISS:	5478497
ISSN:	0965-9978
Views:	3305
Downloads:	1102
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	rotacije;kotna hitrost;integracije po času;kvaternioni;metoda Runge-Kutta;metoda midpoint;
File type:	application/pdf
Type (COBISS):	Not categorized
Pages:	str. 723-733
Volume:	ǂLetn. ǂ42
Issue:	ǂšt. ǂ9
Chronology:	sept. 2011
DOI:	10.1016/j.advengsoft.2011.05.010
ID:	8312577