asrotaties

Asrotaties are the rotations of a rigid body about a fixed axis in three-dimensional space. The axis is defined by a direction and, in some contexts, a line that passes through a point. The rotation is described by an angle measuring how far the body has turned around that axis. In mathematics, all such axis rotations form part of the special orthogonal group SO(3). They can be represented by rotation matrices, unit quaternions, or axis-angle pairs (axis and angle); Rodrigues' rotation formula gives a direct computation from axis and angle to a rotation matrix.

Common examples include turning a wheel around its axle or the rotation of the Earth about its rotational axis. In physics, axis rotations are associated with angular velocity vectors and angular momentum; changes in orientation are driven by torque producing angular acceleration about the axis.

When multiple axes are involved, as in aerospace or robotics, complex motions can be described as a sequence of axis rotations. Using Euler angles to describe such sequences can lead to gimbal lock, whereas axis-angle or quaternion representations avoid some of these issues.

Note: The term asrotaties is primarily used in Dutch-language technical writing; in English, axis rotations or rotations about a fixed axis are more common.

See also: axis-angle representation, Euler angles, rotation matrix, quaternion, SO(3).