Rotieren

Rotieren denotes motion around an axis, resulting in a change of orientation for an object while its overall position may remain fixed. In everyday language it is often used synonymously with turning or spinning.

In physics, rotation is a rigid-body motion about an axis. It is described by angular displacement θ, angular velocity ω = dθ/dt, and angular acceleration α = dω/dt. The axis orientation, direction of rotation, and energy considerations are important, and the right-hand rule provides a convention for positive rotation.

In mathematics, rotations form structured groups. In two dimensions, a rotation by θ is represented by the 2x2 matrix R(θ). In three dimensions, rotations can be expressed through matrices, Euler angles, axis-angle representations, or quaternions. The composition of rotations corresponds to matrix multiplication or quaternion multiplication, and these representations are used to preserve orientation without translational movement.

Applications of rotation span several disciplines. In astronomy, planetary and stellar rotations influence climate, orbital dynamics, and timekeeping. In engineering and mechanics, rotating parts such as shafts, gears, and turbines are analyzed for balance, stiffness, and longevity. In computer graphics and robotics, rotations transform coordinates and animate objects; in crystallography and chemistry, rotational symmetry describes invariance under certain angles.

Rotieren is the German term for the concept, with equivalents in many languages. Related topics include rotational motion, angular momentum, moment of inertia, and the radian as a unit of angular measure.