NAFFO: A numerical algorithm to simulate the damped rotation of synchronous satellites

We hereby introduce and study an algorithm able to determinate the initial conditions corresponding to the equilibrium rotational motion of tidally evolved natural satellites locked in spin-orbit resonance, hereby named Namur Algorithm For Forced Oscillations, NAFFO for short. NAFFO is based on the Numerical Analysis of the Fundamental Frequencies algorithm by J. Laskar, for the identification of the free and forced oscillations, the former being iteratively removed from the solution by carefully choosing the initial conditions. We proved the convergence of the algorithm under suitable assumptions, satisfied in the Hamiltonian framework whenever the d'Alembert characteristic holds true. In that case, the convergence is quadratic.