Article
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Preserved in Portico This version is not peer-reviewed
Vehicle Directional Cosine Calculation Method
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Version 1
: Received: 13 November 2022 / Approved: 18 November 2022 / Online: 18 November 2022 (02:16:41 CET)
A peer-reviewed article of this Preprint also exists.
Hall, D.; Sands, T. Vehicle Directional Cosine Calculation Method. Vehicles 2023, 5, 114-132. Hall, D.; Sands, T. Vehicle Directional Cosine Calculation Method. Vehicles 2023, 5, 114-132.
Abstract
Teaching kinematic rotations is a daunting task for even some of the most advanced mathematical minds. However, envisioning and explaining the three-dimensional rotations can be highly simplified by changing the paradigm. This paradigm change allows for a high school student with a understanding of geometry to be able to not only develop the matrix but also explain the rotations at a collegiate level. The proposed method includes the assumption of a point (P) within the initial three-dimensional frame with axes (x ̂_i, y ̂_i, z ̂_i). It then utilizes a two-dimensional rotation view (2DRV) to measure how the coordinates of point P translate after the initial axis is rotated instead of using the established Euler's formula. The equations are used in matrix notation to develop a direction cosine matrix (DCM) for future equations. This method provides a high school student with an elementary and repeatable process to compose and explain kinematic rotations.
Keywords
kinematics; direction cosine matrixes; education
Subject
Computer Science and Mathematics, Mathematics
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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