Numerical simulation of a rigid rotating body by Obrechkoff integration Original Research Article

It is first supposed that Eulerʹs differential equations for the rotational dynamics of a rigid body have been solved, so that the angular velocity vector for the body and the derivative thereof are known vector-valued functions of time in a body-fixed coordinate system. A method is discussed by which a set of ordinary differential equations (ODEs) may be numerically integrated to deduce the orientation of the body in an inertial frame. The method employs a quaternion formulation for the orientation of the body, exhibits a local truncation error which is typically of fifth order, adheres to the boundary of the region of absolute stability, and requires only one angular velocity evaluation and one angular acceleration evaluation each step. It is then supposed that the solution to Eulerʹs equations for a given body is not known. An interative process is obtained for the integration of Eulerʹs equations and the ODEs for body orientation simultaneously.