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Numerical algorithm for quaternion integration based on three independent parameters with no need for re-normalization

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Abstract

The relative attitude change determined from the beginning of each time step to its end defines a relative quaternion. This relative attitude is characterized by only three independent quaterion parameters, with a closed form expression for a fourth dependent parameter as a function of the independent parameters. This procedure ensures that each estimate of attitude is automatically based on a unit quaternion without the need for re-normalization. An example of a complicated three-dimensional motion is used to show that there is no loss in accuracy relative to standard unit and non-unit formulations. Also, an example of Euler integration is used to demonstrate distortion of the rotation matrix due to re-normalization.

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    M. B. Rubin

  2. RAFAEL, PO Box 3102102, Haifa, Israel

    H. Weiss

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  1. M. B. Rubin
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Rubin, M.B., Weiss, H. Numerical algorithm for quaternion integration based on three independent parameters with no need for re-normalization. Acta Mech 234, 2009–2020 (2023). https://doi.org/10.1007/s00707-023-03473-x

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