CardanWinkel

CardanWinkel, also known as Euler angles, are a set of three angles used to describe the orientation of a rigid body in three-dimensional space. They represent a sequence of rotations around the principal axes of the body. Imagine a coordinate system fixed to the body and another fixed in space. CardanWinkel define how the body's coordinate system is rotated relative to the fixed system.

The specific order of rotations matters. Common conventions include Z-Y-X, X-Y-Z, or Z-X-Z. For example, in a Z-Y-X convention, the first rotation is around the Z-axis, the second around the *new* Y-axis, and the third around the *newest* X-axis. Each rotation is defined by an angle.

While intuitive for describing sequential rotations, CardanWinkel suffer from a phenomenon known as gimbal lock. This occurs when the middle rotation aligns the first and third axes, effectively reducing the degrees of freedom and making it impossible to achieve certain orientations. This can be a significant problem in applications like flight simulators or robotics. Alternatives like quaternions are often used to avoid gimbal lock. Despite this limitation, CardanWinkel remain a useful tool for understanding and representing rotations in many contexts.