2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143229We reduced the problem of constructing bi-Hamiltonian structure in three dimensions to the solution of a Riccati equation in moving coordinates of Serret-Frenet frame. We then show that either the linearly independent solutions of the corresponding second order equation or the normal vectors of the moving frame imply two compatible Poisson structures.Mathematical Physicstext