“…On the other hand, when looking for new selected trajectories in Celestial Machanics, one often seeks minimizers of the action in some set of functions sharing a prescribed topological behaviour, as, for example, in [6,7,12,13,14,20,24,25]. In such a situations, Marchal's lemma cannot be employed because the average argument may destroy the topological constraint, and this, usually, makes impossible to deduce any conclusive information.…”