Vehicle Directional Cosine Calculation Method

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.