| A normalized form of Euler's equations is rewritten using a variation of parameters approach with amplitudes and angular displacement as parameters. This new form is compact and yields a much more accurate numerically integrated solution over longer simulation intervals than a conventional integration of Euler's equations. The complete variation of parameters formulation involves the classical Jacobian elliptic functions as well as standard elliptic integrals. Since this formulation is developed in tree fixed reference frame of the body's principal axes, these variation of parameters equations can be simply grouped with the dynamical equations for rotation, i.e. the variation of the Euler-Rodrigues parameters, to provide singularity free information about the attitude of the body in a. local inertial reference frame. This formulation is then compared to the traditional formulation in the normalized body-frame and for a simple, gravity-gradient stabilized satellite to investigate error propagation behaviour in computer simulations. |
