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accuracy Ae)t M(Ot Ae)t_h algebraic constraint angle Bo ANGLE BQ Figure angles and quaternions angular speed attitude error rate basis quaternions benchmark problem Benjamin G Chun Fang computer solutions constraint equation constraint error rate constraint error reduction constraint technique critical angle Bo cycle derivative constraint differential equations DIGITAL SIMULATION emax Equa Equation 16 equation in Equation error per step errors i.e errors introduced estimated error Euler angles evaluated Fang and Benjamin Goddard Space Flight gration technique Greenbelt increase in simulation indicates integration step Kutta Merson integration M(e)t_h mathematical model maximum moving axis system moving system nique NORMALIZED CONSTRAINT obtained optimum quaternion components radians reducing the constraint renormalized rigid body ROTATIONAL KINEMATICS Runge Kutta Merson SDS 9300 computer SIMULATION SPEED cycle/sec simulations involve solutions sinB singularity Space Flight Center stability condition stable value step size criterion step size h techniques for reducing transformation matrix variable variable-step technique