Kinematic equations of a rigid body in four-dimensional skew-symmetric operators and their application in inertial navigation

Abstract

Abstract New dual matrix and biquaternion kinematic equations of motion of a free rigid body in dual four-dimensional matrix and biquaternion skew-symmetric operators are proposed. The equations are constructed using dual matrix and biquaternion analogues of Cayley's formulae, which are used to match a dual four-dimensional matrix operator and a biquaternion skew-symmetric operator to a classical biquaternion four-dimensional matrix and the biquaternion of a finite screw displacement of a free rigid body. New quaternion and biquaternion formulae for the summation of finite rotations and finite screw displacements of a free rigid body in four-dimensional skew-symmetric operators are also proposed. The proposed equations and formulae are constructed using the Kotelnikov–Study transference principle. The use of the proposed real and dual matrix kinematic equations of motion, as well as quaternion and biquaternion kinematic equations of motion, of a rigid body to construct new high-precision algorithms for operating strapdown inertial navigation systems is discussed.