Now if he were to locate an airplane instead (it is quite unlikely that he would find one in that desolate paradise of his!) he would require another ‘rotation’ value to specify its orientation. Think of it, just pointing to the airplane as if it were a star will not tell the direction it is travelling in. That validates the necessity for a third parameter. The lesson learnt from the story is this- for completely specifying the orientation of an ‘extended object’ like the airplane with respect to a reference frame, three rotation parameters are a minimum. <br \>

Where does this come into the satellite picture? Remember, the attitude of a satellite (an ‘extended’ object) gives its (more specially, its body frame’s) orientation with respect to a reference frame. And this requires three rotation parameters. Euler angles captures this idea. This is a set of three ‘ordered’ rotation parameters. So, each parameter corresponds to rotation about a specific axis the new coordinate system obtained post rotation. Each rotation is mathematically represented by a rotation matrix. And matrix multiplication of three rotation matrices (again, order is important) gives the net rotation.<br \>

Shown above is a rotation following a particular convention of (Ф,Ө,ψ), the angles being rotation about (z,x,z) axes respectively. The rotation matrix A then is,<ref>http://mathworld.wolfram.com/EulerAngles.html</ref>

[[File:Equation67.png|frame|center]]