Rotasjonsformel

Rotasjonsformel refers to a mathematical formula used to describe the rotation of an object or coordinate system. In a two-dimensional Cartesian coordinate system, a point (x, y) rotated by an angle θ counterclockwise around the origin (0,0) results in a new point (x', y'). The formulas for these new coordinates are x' = x cos(θ) - y sin(θ) and y' = x sin(θ) + y cos(θ). These equations are derived using trigonometry and the concept of polar coordinates.

The rotasjonsformel is fundamental in various fields, including computer graphics, physics, and engineering. In computer graphics, it is used for animating objects, transforming images, and rendering scenes. In physics, it appears in the study of rotational motion, angular momentum, and the transformation of physical quantities between different inertial frames of reference. For example, when analyzing the motion of a spinning rigid body, these formulas are essential for relating velocities and accelerations in a rotating frame to those in a stationary frame.

The concept can be extended to three dimensions, where rotations are more complex and can be represented using matrices or quaternions. In three dimensions, a rotation is defined by an axis of rotation and an angle of rotation. The rotasjonsformel in 3D ensures that all points of a rigid body rotate consistently around the specified axis. This generalization is critical for simulating complex physical systems and creating realistic 3D environments.