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Hi, Now I understood. In the above picture, they have the vector fixed and rotated the axes. I couldn't understood it at first. Thank you for your answer :)fresh_42 said:
Yes it is. Here they rotated the axes instead of vector.WWGD said:
Yeah, this is really a bit difficult to distinguish sometimes: changing the coordinates or changing the object and how does it affect the matrix? It's easy to get confused if one doesn't keep track of what is what and in which coordinate system. A tip is better to write some extra lines than to search for errors afterwards. I always tell students when it comes to calculations: write it down step by step, because writing is fast, thinking is slow.Leo Authersh said:
I believe thinking is fast. But if we write down each step we can save all the cognition for solving a specific step which otherwise would be wasted in memorizing the already solved steps. But that's just for me :)fresh_42 said:
Rotation matrices are mathematical tools used to describe the rotation of an object in three-dimensional space. They are used in various scientific fields such as physics, engineering, computer graphics, and robotics to model and manipulate the rotation of objects.
Rotation matrices work by representing rotations in terms of three basic rotations around the x, y, and z axes. These rotations can be combined to create any desired rotation in three-dimensional space. Each rotation is described by a 3x3 matrix, where the columns represent the new orientation of the x, y, and z axes after the rotation.
A rotation matrix is a type of transformation matrix that represents only rotations in three-dimensional space. Transformation matrices, on the other hand, can include other types of transformations such as translations, scaling, and shearing. Rotation matrices are a subset of transformation matrices.
Rotation matrices can be visualized geometrically by applying them to a set of points or vectors in three-dimensional space. The resulting points or vectors will be rotated according to the rotation matrix. Additionally, rotation matrices can be visualized using a 3D coordinate system, where each axis represents the direction of rotation for that particular rotation matrix.
Rotation matrices have numerous real-world applications, such as in computer graphics to rotate images or objects, in robotics to control the orientation of robotic arms, in physics to describe the rotation of rigid bodies, and in navigation systems to track the orientation of objects in space. They are also used in video games, animation, and virtual reality to simulate realistic movements and rotations of objects.
