Numerical Integration of Quaternion Kinematics Using Collocation Method

Abstract

In many aerospace applications, long-term attitude propagation is frequently involved. Because the integration error accumulates, the accuracy of the integration scheme is more important for the long-term attitude propagation problems. In this study, instead of explicit integration methods that have been extensively employed, the collocation method for the attitude propagation problem is studied to improve numerical integration accuracy. The closed-form solution for the collocation conditions imposed at the collocation points is derived to avoid iterative process in the collocation method. In the derivation, the operational matrix of differentiation and the Legendre-Gauss-Lobatto quadrature rule are used. Through numerical examples, the accuracy of the proposed collocation method is compared with those of the explicit methods.