Cayley-Klein parameters
A set of four complex numbers used to specify the orientation of a body, or equivalently, the rotation R which produces that orientation, starting from some reference orientation. They can be expressed in terms of the Euler angles ψ, Θ, and &phgr;, as in the equations below. 
Although these parameters have been used to simplify somewhat the mathematics of spinning top motion, their main use is in quantum mechanics. There they are related to the Pauli spin matrices and represent the change in the spin state of an electron or other particle of half-integer spin under the space rotation R (ψ, Θ, &phgr;). See Spin (quantum mechanics)
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