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22:35
YouTube
Physics Ninja
Rotation Matrix for 2D Vectors
Physics Ninja looks at the derivation for the 2D rotation matrix. The matrix allows us to calculate the new components of a vector that has been rotated by some angle. Both counter-clockwise and clockwise directions are considered. Previous video link: Rotation Matrix for Coordinate Transformation https://www.youtube.com/watch?v=-HcDl_gyeMs
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In 3D, rotation matrices are used to rotate objects around the x, y, or z axes. Each axis has its own specific rotation matrix. For example, rotating around the z-axis uses a matrix that leaves the z-coordinate unchanged but rotates the x and y coordinates, effectively spinning the object in the xy-plane. Similarly, rotating around the x-axis affects the y and z values, while rotating around the y-axis affects the x and z values. These 3x3 matrices are always orthogonal, meaning their rows and c
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