2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58087In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian flows. To illustrate our scheme and factorization theory, we consider a family of hyperbolic spin Ruijsenaars-Schneider models related to affine Toda field theories and solve the equations of motion in a simple case.22 pages. This version has additional typo correctionsMathematical PhysicsSymplectic Geometrytext