Technical Note
Version 1
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Linearized Expressions of 3D Rotational Motion
Version 1
: Received: 11 May 2024 / Approved: 13 May 2024 / Online: 14 May 2024 (14:56:20 CEST)
How to cite: Liu, Y. Linearized Expressions of 3D Rotational Motion. Preprints 2024, 2024050982. https://doi.org/10.20944/preprints202405.0982.v1 Liu, Y. Linearized Expressions of 3D Rotational Motion. Preprints 2024, 2024050982. https://doi.org/10.20944/preprints202405.0982.v1
Abstract
Rotation motion in a three-dimensional physical world refers to an angular displacement of an object around a specific axis in $\mathbb{R}^3$. It is typically formulated as a non-linear and non-convex process due to the nonlinearity and nonconvexity of $\mathbb{SO}(3)$. However, this paper proposes a new perspective that the 3D rotation motion can be expressed by the linear equation without dropping any constraints and increasing any singularities. Moreover, two frequent cases, i.e., $\angle\left(\mathbf{R}\boldsymbol{x},\boldsymbol{y}\right)=0(\pi)$ and $\angle\left(\mathbf{R}\boldsymbol{x},\boldsymbol{y}\right)=\frac{\pi}{2}$, in computer vision and robotics that can be expressed linearly are deeply discussed in this paper.
Keywords
Rotation motion
Subject
Computer Science and Mathematics, Robotics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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