Equilibrium search algorithm of a perturbed quasi-integrable system: NAFFO: Numerical Algorithm For Forced Oscillations

We hereby introduce and study an algorithm able to search for initial conditions corresponding to orbits presenting forced oscillations terms only, namely to completely remove the free or proper oscillating part, 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. We provided two relevant applications: the spin-orbit problem and the forced prey-predator problem.