Analytical Solution of an Approximate Equation for the Vector of a Rigid Body Finite Rotation and its Application to Construct the Algorithm for Determining the Strapdown INS Orientation

The analytical solution of an approximate equation for the vector of a rigid body finite rotation has made it possible to solve the problem of determining the quaternion of orientation of a rigid body for an arbitrary angular velocity and small angle of rotation of a rigid body with the help of quadratures. Proceeding from this solution, the following approach to the design of a new algorithm for computation of strapdown INS orientation is proposed.