Rotation Matrix Tutorial for Robotics and Aerospace - Z rotation - Complete Derivation

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In this robotics, GNC, and aerospace tutorial, we explain the concept of rotation matrices. We consider the case of rotation of two coordinate systems with respect to the Z axis. By using vector calculus we derive the expression for the z-rotation matrix. We explain how the rotation matrices are used to convert vector representations from one coordinate system to another. We then explain that the rotation matrices are orthogonal. We also provide a clear graphical explanation of rotation matrices.

Rotation matrices are very important in robotics, aerospace engineering, and guidance, navigation, and control. I noticed that it is a common misconception among students studying robotics and aerospace that rotation matrices are actually rotating vectors. They are not rotating vectors, they are the consequence of two coordinate systems rotated with respect to each other. Usually, the so-called body coordinate system is fixed to the rotating object, and rotation matrices are used to transform the coordinates of a vector from the body frame to some other (usually inertial) frame. Here is the tutorial I made that explains

1.) What are the rotation matrices.
2.) How to derive them.
3.) How they are used to transform coordinates from one coordinate system to another.

[aleksandarhaber]

It takes a significant amount of time and energy to create these free video tutorials. You can support my efforts in this way:
- You Can also press the Thanks YouTube Dollar button