Abstract
In this paper an algorithm is presented to expand any Lie monomial in the Ph. Hall basis. The algorithm exploits an algorithm for the optimal generation of Ph. Hall basis and it can be used to express \(\log (\exp \, X \cdot \exp \, Y)\) in this basis. An explicit formula for the logarithm includes the Ph. Hall elements up to the 7th degree. The Ph. Hall expansion is useful in the theory of Lie algebras and in robotics for nonholonomic motion planning.
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Duleba, I., Karcz-Duleba, I. (2020). Algorithm to Express Lie Monomials in Ph. Hall Basis and Its Practical Applications. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2019. EUROCAST 2019. Lecture Notes in Computer Science(), vol 12013. Springer, Cham. https://doi.org/10.1007/978-3-030-45093-9_56
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DOI: https://doi.org/10.1007/978-3-030-45093-9_56
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