Averaging techniques are often used to analyze the slow dynamics in dynamical systems admitting slow and fast variables, in particular in celestial mechanics (lunar theory). More recently, they were introduced in optimal control to analyze the orbital tranfer of a satellite using low propulsion and get a complete analytical description of the motion in the energy minimization problem using averaging with respect to the longitude.
Those results have to be extented in several directions motivated in particular by more complicated models taking into account standard perturbations in space mechanics e.g. lunar and solar attraction, earth oblatness…
This leads to averaging with several angular variables (and problems related to convergence of the averaged system due to small denominators, resonances), or to time-varying averaging. Both theoretical and numerical explorations have to be conducted.
