The spacecraft is oriented by picking axes in the geometry of the spacecraft in the Spacecraft Axes feature, and then specifying what these axes should be oriented towards in the Spacecraft Orientation feature. The spacecraft can rotate about one, two, or all three axes and there can be parts of the spacecraft that articulate. Articulation is modeled via the Moving Mesh interface.

The primary and secondary axis specified by the user in the Spacecraft Axes feature are eSPA and eSSA, respectively. They might not be orthogonal so a third vector is defined as: . From that, the secondary axis is redefined to form an orthonormal basis: . These three vectors form the columns of the orthonormal matrix that transforms from the spacecraft coordinate system (SCS) to the material coordinate system:

The primary and secondary orientation specified by the user in the Spacecraft Orientation feature are eP,t and eS,t, respectively. They form a set of temporary vectors that might not be orthogonal so a third temporary vector is defined: . From that, the temporary secondary orientation is redefined to form an orthonormal basis: .

These vectors are referred to as temporary vectors, because the spacecraft may be rotating about these three, so we have to define a set of three consecutive rotations about them, using the Rodrigues’ rotation formula. Given a set of rotation angles, ωp, ωs, ωt, about the temporary primary, secondary, and third orientation vectors of the SCS, the first rotation gives the vectors:

The second rotation is about eS,t:

The third rotation about eT,t gives the primary, secondary and third orientation vectors: