On the Secular Behavior of Irregular Satellites
  Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies occur because in secular theories the disturbing function is averaged over orbital motions, whereas instead one should take into account some large periodic terms, most notably the so-called ``evection''. We demonstrate that such terms can be incorporated into the Kozai formalism, and that our synthetic approach produces much better agreement with results from symplectic integrations. Using this method, we plot the locations of secular resonances in the orbital-element space, and we note that the distribution of irregular satellite clusters appears to be non-random. We find that the large majority of irregular-satellite groups cluster close to the secular resonances, with several objects having practically stationary pericenters. None of the largest satellites belong to this class, so we argue that this dichotomy implies that the smaller near-resonant satellites might have been captured differently than the largest irregulars. 
Matija Cuk, Joseph A. Burns (Cornell U.)