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A 4th-Order Variational Problem on SO(3)

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CONTROLO 2022 (CONTROLO 2022)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 930))

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Abstract

In this paper we consider a invariant fourth-order variational problem on SO(3) and study its stationary points by means of the Euler-Poincaré reduction. This gives rise to a generalization of Euclidean septic polynomials to SO(3) and provides a higher-order interpolation method that is one step ahead of the cubic interpolation method for rotations in space.

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Acknowledgments

The author thanks the anonymous referees for constructive comments and suggestions that contributed to improve the quality of the paper. This work was partially supported by the Centre for Mathematics of the University of Coimbra - UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES.

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Authors and Affiliations

  1. University of Coimbra, CMUC, Department of Mathematics, 3001-501, Coimbra, Portugal

    Margarida Camarinha

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  1. Margarida Camarinha
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Correspondence to Margarida Camarinha .

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Editors and Affiliations

  1. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Luís Brito Palma

  2. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Rui Neves-Silva

  3. Electrical and Computer Engineering Department, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal

    Luís Gomes

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Camarinha, M. (2022). A 4th-Order Variational Problem on SO(3). In: Brito Palma, L., Neves-Silva, R., Gomes, L. (eds) CONTROLO 2022. CONTROLO 2022. Lecture Notes in Electrical Engineering, vol 930. Springer, Cham. https://doi.org/10.1007/978-3-031-10047-5_31

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