Rotací

Rotací is a term used in some technical contexts to denote the study of rotational motion and orientation in physical and engineered systems. It focuses on how objects rotate about axes, how these rotations compose, and how they are measured and controlled over time. In practice, rotací uses several representations of orientation: Euler angles (three angles describing consecutive rotations about coordinate axes), rotation matrices, and unit quaternions. The instantaneous rate of rotation is described by the angular velocity vector ω, while the rate of change of ω is angular acceleration α. Mathematically, rotations in three dimensions form the Lie group SO(3); small rotations are described by the Lie algebra so(3). The exponential map connects angular velocity to finite rotations, providing a bridge between continuous motion and discrete update steps in simulations and control systems.

Rotací has wide applications in robotics, aerospace, computer graphics, and mechanical systems with moving parts. In robotics, joint controllers regulate rotational motion to achieve precise pose. In spacecraft attitude control, orientation is maintained or changed using actuators and sensor feedback. In computer graphics, rotations are used to animate objects and cameras. Practical measurement relies on devices such as gyroscopes and inertial measurement units, which provide angular velocity data that is integrated to update orientation; corrections are applied to counter drift and biases.

Common challenges include gimbal lock in Euler representations, numerical drift in integration, and the non-commutative nature of composing rotations. By choosing appropriate representations—quaternions or rotation matrices—these issues can be mitigated.

See also: rotation, SO(3), quaternions, Euler angles, gyroscope.