## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Generalized Euler Angles Viewed as Spherical Coordinates

#### 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

Dates
First available in Project Euclid: 14 January 2017

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