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\begin{document}

\title{The Order of Finite Generation of SO(3) and Optimization of Rotation
Sequences}



\author[1]{Danail Brezov}%
\affil[1]{Universitet po arhitektura stroitelstvo i geodezia Katedra Matematika}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
We generalize an old result due to Lowenthal {[}1{]} and a more recent
one due to Hamada {[}2{]} on the order of finite generation of the
rotation group SO ( 3 ) both for fixed and arbitrary compound
transformations. Unlike the above cited authors, we consider
decompositions into factors with more than two invariant axes and
provide rather intuitive geometric proofs. Thus, we derive a simple
estimate for the number of factors in a decomposition and discuss
possible means of optimization as well as particular examples of
potential interest for the applications.%
\end{abstract}%



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