Tensor Analysis of Finite Rotations: Applications to Aircraft Manoeuvres, Variable Sweep Wings, Retractable Undercarriages

The orientation of a rigid body is described by a position‐tensor, composed of three unit vector axes fixed in the body; rotation is effected by tensor transformations in which a rotational operator is a Cartesian matrix, formed from the co‐ordinates of the pivot axis and components of the angle of rotation; rotational sequences are represented by matrix products. Three practical applications are discussed: sequences of aircraft manoeuvres, which include composite rotations of roll and pitch, or roll, pitch and yaw, applied simultaneously; the variation of sweep, incidence and dihedral of a wing moving on any axis fixed in the aircraft; the direction of the pivot axis and the angle of rotation in the motion of a retractable undercarriage between two specified positions.