Measuring and solving real coning motion of spinning carriers

Coning motion of spinning carriers is a complex rotating motion with various forms that include single circular motion, double circular motion and multiple circular motion. Due to the fact that it is difficult to describe the real coning motion of double circular motion and multiple circular motion by the common method of attack angle and sideslip angle (A–S), a cone frame and cone angles are defined to describe coning motion. Through analysis of measuring the relationship between coning motion and inertial devices such as gyroscopes and accelerometers, an inertial measuring method is proposed to build the measuring equation and resolving equation. A geometry-solving algorithm of real coning motion is derived in detail, and radiuses of large circle and real cone circle are obtained as well. A flight simulation of a spinning carrier with coning motion is designed and used to verify the measuring method and the geometry-solving algorithm. The result shows that: (1) the inertial measuring method has the same validity as A–S method to describe coning motion, but is superior to A–S method for the reason of providing the rotation information of carriers; (2) due to coupling relationship, the rotating angle is equal to the subtraction of roll angle and precession angle; (3) the real precession angle and the real nutation angle are calculated by the geometry-solving algorithm, and the real coning motion is obtained finally.