Rotatsiya

Rotatsiya, from the Russian word ротация (rotation), is the term used in several languages to denote the act or result of turning around an axis or central point. It encompasses a wide range of phenomena in science, engineering, and everyday use, including the spin of objects, the turning of positions or orientations, and the cyclical repetition of processes.

In mathematics and geometry, a rotation is a rigid motion that preserves distances and angles. In the plane, rotating a point by angle θ about the origin is described by the matrix [ [cos θ, -sin θ], [sin θ, cos θ] ]. In three dimensions, rotations occur about an axis and can be represented by axis–angle, Euler angles, or unit quaternions; the set of all 3D rotations forms the group SO(3).

In physics, rotational motion is characterized by angular velocity and angular momentum. Torque changes angular momentum according to τ = dL/dt, and for a fixed axis, torque equals the moment of inertia times angular acceleration: τ = Iα. Rotations interact with translational motion in complex systems and are fundamental to the study of dynamics.

In technology and computer science, rotations are used to orient objects, render scenes, and model motion. Quaternions are often preferred for representing rotations in 3D computer graphics because they avoid gimbal lock and allow smooth interpolation (SLERP) between orientations.

In astronomy and geophysics, the rotation of planets and stars governs day lengths, tidal interactions, and rotational dynamics that influence observational timing and orbital evolution. Rotatsiya thus denotes a basic and widely applicable concept of turning around an axis across disciplines.