STODOLA, M. Geometric algebras for Euclidean geometry [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2024.
The thesis deals with GA variants suitable for working with Euclidean geometry of three-dimensional space. The introductory chapters show how to find a suitable GA to the chosen Lie algebra of infinitesimal symmetries. This way, the algebras G3, PGA, CGA, and their 2D variants are constructed sequentially. This is followed by a chapter introducing these algebras as subalgebras of the CGA algebra and discussing suitable representations of the geometric objects. An additional chapter shows how to use the apparatus of dual spaces. The last chapter shows how to model higher GAs, namely GAC, on the existing apparatus. The work is based on a non-trivial mathematical theory that is clearly defined and explained. The actual GA embedding contains new, non-trivial insights into how all the artificial algebras could be used to solve a concrete example. This is demonstrated with a concrete example of a SCARA robot model. In particular, the work is devoted to solving a 2D problem in 3D, which motivated the choice of the mentioned kinematics. The thesis contains no factual errors and has a clear structure. A series of implementations show that the proposed apparatus is workable and efficient
viz. posudek v PDF
viz. posudek v PDF
eVSKP id 163067