vinkelendringen

Vinkelendringen (Norwegian for "the change in angle") denotes the difference between two angular orientations of a line, vector, joint or trajectory. In its simplest discrete form it is computed as the final angle minus the initial angle and is commonly expressed in degrees or radians. Sign conventions vary by context; a positive vinkelendring often indicates counterclockwise rotation and a negative value clockwise rotation.

In geometry and polygonal chains, vinkelendringer at vertices describe how a path turns; the sum of the exterior vinkelendringer along a simple closed curve equals 360 degrees (2π radians). In continuous settings, the instantaneous rate of vinkelendring along a curve is curvature, and the total vinkelendring over a curve segment equals the integral of curvature with respect to arc length.

Practical applications include navigation and surveying (course changes or bearing differences), robotics and biomechanics (joint rotations and link orientations), computer graphics and animation (object rotations and camera turns), and road or railway design (alignment and transition curves). Measurement can be performed directly with angular encoders, compasses, gyroscopes, or inferred from coordinate data using inverse trigonometric functions, taking care to handle branch cuts and wraparound from 360 to 0 degrees.

Understanding vinkelendringen is important for analyzing motion, ensuring smooth transitions, and computing geometric properties of paths and mechanisms.