(Hindawi Publishing Corporation, 2009) Lara, Martín; Palacián Subiela, Jesús Francisco; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that connects the averaged and nonaveraged models. A fourth-order analytical theory is necessary for the accurate computation of quasi-periodic frozen orbits.