Integrating rotation from angular velocity

Zupan, Eva (author), Saje, Miran (author)

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.

• Language: English
• Keywords: rotation, angular velocity, time integrations, quaternions, Runge-Kutta method, midpoint rule
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publisher: Elsevier
• Year: 2011
• Number of pages: Str. 723-733
• Numbering: Letn. 42, št. 9
• PID: 20.500.12556/RUL-32177
• UDC: 624.07
• ISSN on article: 0965-9978
• DOI: 10.1016/j.advengsoft.2011.05.010
• COBISS.SI-ID: 5478497
• Publication date in RUL: 10.07.2015

Record is a part of a journal

• Title: Advances in engineering software
• Shortened title: Adv. eng. softw.
• Publisher: Elsevier Applied Science
• ISSN: 0965-9978
• COBISS.SI-ID: 34540032

Secondary language

• Language: English
• Keywords: rotacije, kotna hitrost, integracije po času, kvaternioni, metoda Runge-Kutta, metoda midpoint