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[[File:Equation1.gif|frame|center]]
In the rotation we have made above, Ф and ψ have lost their unique identities. There are multiple values we could use to obtain the same result (as long as Ф +ψ is the same). Here, we have lost a degree of freedom, only two independent parameters are required to represent this rotation. In a mathematical sense, this is a problem, because we don’t have unique Ф and ψ values at hand. <br \>
Quaternions is an alternative to Euler angles. It uses the fact that one unique axis and a rotation about it can do this job. It is, in fact, more intuitive.<br \>==References ==http://mathworld.wolfram.com/EulerAngles.html
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