Bounding the rotation formula's switch

The native motion calculation uses a short polynomial for very small rotation increments and a trigonometric formula for larger ones. A calibration range can cross that switch. Treating the whole range as one smooth formula would miss a small change between the two expressions.

A separate component now encloses both formulas and bounds that change through third derivative order. Three checks pass against independent scalar polynomial and trigonometric references. The small-angle result retains the native polynomial rather than replacing it with an exactly orthogonal rotation.

This covers one local switch for a smooth supplied input path. It does not cover incoming jumps, propagate changes through a whole flight, establish clock-boundary completeness or bound native floating-point execution. It is not installed in either running study.

Mathematics · Trajectory components · Prediction requirements