Developments on the Jordan-Schwinger construction and contraction for the $su_q(2)$

The contraction and Jordan-Schwinger construction connect the su(2) and the heisenberg algebra, going in oposite directions. This persists in the q-deformed cases, but in a slightly different way. This work investigates this further, discussing some details and results found in the litterature and presenting some new ones, including a nonlinear choice for the contraction.