ABSTRACT
Euler angles and quaternions are commonly used ones for spacecraft attitude representation among them, whereas Gibbs vector and modified Rodrigues parameters, which are derived from quaternions, are especially favorable in attitude filtering. The formula for obtaining quaternion vector by the use of the Euler angles is given as Note that 3-2-1 sequence is used for representing the attitude in Euler angles here. Expressions for the Gibbs vector components in terms of the direction cosine matrix elements can be defined. Although the Gibbs vector itself is not widely used in aerospace applications, it may be preferred as an attitude error representation, especially when an attitude filter is being designed. As it has minimal set for attitude representation, attitude can be represented without any constraint in this case in contrast to the quaternions. A transformation from one coordinate frame to another can be carried out by three consecutive rotations about different axes.
