Proceedings of the International Conference on Geometry, Integrability and Quantization

Generalized Euler Angles Viewed as Spherical Coordinates

Danail S. Brezov, Clementina D. Mladenova, and Ivaïlo M. Mladenov

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Here we develop a specific factorization technique for rotations in $\mathbb{R}^3$ into five factors about two or three fixed axes. Although not always providing the most efficient solution, the method allows for avoiding gimbal lock singularities and decouples the dependence on the invariant axis ${\bf n}$ and the angle $\phi$ of the compound rotation. In particular, the solutions in the classical Euler setting are given directly by the angle of rotation $\phi$ and the coordinates of the unit vector $\bf{n}$ without additional calculations. The immediate implementations in rigid body kinematics are also discussed and some generalizations and potential applications in other branches of science and technology are pointed out as well.

Article information

Source
Proceedings of the Eighteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Guowu Meng and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2017), 105-116

Dates
First available in Project Euclid: 14 January 2017

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1484362818

Digital Object Identifier
doi:10.7546/giq-18-2017-105-116

Mathematical Reviews number (MathSciNet)
MR3616915

Zentralblatt MATH identifier
1380.53017

Citation

Brezov, Danail S.; Mladenova, Clementina D.; Mladenov, Ivaïlo M. Generalized Euler Angles Viewed as Spherical Coordinates. Proceedings of the Eighteenth International Conference on Geometry, Integrability and Quantization, 105--116, Avangard Prima, Sofia, Bulgaria, 2017. doi:10.7546/giq-18-2017-105-116. https://projecteuclid.org/euclid.pgiq/1484362818


Export citation