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Mastering 3D Rotations: The Direction Cosine Matrix (DCM) | Finite Rotation Series (Part 2 of 4)
🚀 Welcome to Part 2 of our four-part mini-series on handling 3D finite rotation in geometric nonlinearities! 🚀 In this video, we break down the Direction Cosine Matrix (DCM)—a fundamental tool for describing 3D rigid body rotations in structural mechanics, aerospace engineering, robotics, and kinematics. This method, originally ...
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3D Rotation Matrix
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
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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