  The collective coordinates expansion of the Skyrme soliton particle model
gives rise to the second class constraints. We use the non-abelian BFFT
formalism to convert this system into the one with only first class
constraints. Choosing two different structure functions of the non-abelian
algebra, we obtain simplified algebraic expressions for the first class
non-abelian Hamiltonians. This result shows that the non-abelian BFFT method
is, in many aspects, richer than the abelian BFFT formalism. For both of the
first class Hamiltonians, we derive the Lagrangians which lead to the new
theory. When one puts the extended phase space variables equal to zero, the
original Skyrmion Lagrangian is reproduced. The method of the Dirac first class
constraints is employed to quantize these two systems. We achieve the same
spectrum, a result which confirms the consistency of the non-abelian BFFT
formalism.
