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

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.