rotasjonsvektoren

A rotasjonsvektor, also known as an axis-angle representation or rotation vector, is a mathematical concept used to describe a rotation in three-dimensional space. It combines two pieces of information: the axis around which the rotation occurs and the angle of that rotation. The direction of the vector represents the axis of rotation, and the magnitude of the vector represents the angle of rotation in radians.

The rotasjonsvektor provides a compact way to represent rotations compared to other methods like Euler angles or rotation matrices. For a rotation by an angle θ around an axis defined by a unit vector u, the rotasjonsvektor v is given by v = θu. This representation is particularly useful in fields like computer graphics, robotics, and physics, where rotations are frequently encountered.

One advantage of the rotasjonsvektor is that it is continuous, meaning that small changes in the rotation correspond to small changes in the rotasjonsvektor. This is not always true for other rotation representations, such as Euler angles, which can suffer from gimbal lock. However, the rotasjonsvektor can be more computationally intensive to work with directly in some operations, such as composing multiple rotations, compared to rotation matrices. Conversions between rotasjonsvektor representation and other rotation representations are well-defined mathematical procedures.