Key Engineering Takeaways
- •Euler angles suffer from Gimbal Lock (loss of 1 degree of freedom when pitch reaches ±90°); Quaternions provide singularity-free representation.
- •A unit quaternion consists of 4 numbers: q = [w, x, y, z] with ||q|| = 1.
- •SLERP smoothly interpolates between two 3D orientations at constant angular velocity.
Prerequisites
- • Complex numbers
- • Vector cross products
Why Quaternions? The Flaws of Euler Angles
In 3D robotics simulation and drone flight control, representing orientation with Roll-Pitch-Yaw (Euler angles) causes catastrophic mathematical singularities whenever the middle gimbal aligns with the outer gimbal, destroying the ability to distinguish pitch from yaw.
Tags:#Quaternions#Rotations#Gimbal Lock#SLERP#SO3#Spatial Math