rotatsioonit

Rotatsioonit is a term found in some Estonian-language mathematical and technical texts to denote the rotation transformation, i.e., the act or result of turning a figure or object around a fixed point or axis. It is closely related to the more common terms rotatsioon and pöörlemine, and in many contexts can be treated as synonymous with rotation. The word emphasizes the process of rotating rather than the object’s state alone.

In two dimensions, rotatsioonit about the origin by angle theta is represented by the rotation matrix R(theta) = [[cos theta, -sin theta], [sin theta, cos theta]]. In three dimensions, rotatsioonit can describe turning around a fixed axis u by angle theta; the orientation change can be expressed via Rodrigues’ formula or equivalent rotation matrices. Rotations preserve distances and angles, making them orthogonal transformations with determinant +1.

Algebraically, the set of all rotatsioonit in a given dimension forms a Lie group: SO(2) for planar rotations and SO(3) for spatial rotations. Rotations compose and have inverses, yielding a continuous, smooth structure suitable for describing rigid-body motion. In practical applications, rotatsioonit are represented in various forms, such as rotation matrices, quaternions, or Euler angles, each with its ownAdvantages and limitations for interpolation and computation.

Common applications include computer graphics, robotics, navigation, physics, and animation, where precise control of orientation and attitude is essential. Related concepts include angular velocity, orientation, and frame transformation. See also rotation matrix, quaternion, Euler angles, and Lie group SO(n).