How can the next supermoon be analytically predicted? The lunar motion can be predicted with basic celestial mechanics, but the perigee and apogee are not always the same, basically because the attraction of the Sun makes some oscilations in the semi-axis of the orbit (https://en.wikipedia.org/wiki/Perturbation_(astronomy)). 

My question is: how do they know when the full moon will get as close as it got in the recent supermoon? For example, the Dailypost article Biggest Supermoon in 68 years will light up the November sky claims that the full moon won't come this close to Earth until November 25th, 2034.
How do they kow that? Are they using the perturbation theory equations to predict this? If so, can anybody give me some source or explanation of how it's done analytically?
A slightly more useful answer than my comment above:

Using http://wgc.jpl.nasa.gov:8080/webgeocalc/#NewCalculation "Angular
Separation Finder" feature, we can determine when the angle between
the Sun and the Moon is at a local maximum. It turns out this isn't
quite the definition of Full Moon, but it's very close. I couldn't
find a way to make webgeocalc compute full moon times exactly, though
I'm sure there is a way, and, of course, there are plenty of tables of
full moons online.

Starting at
http://wgc.jpl.nasa.gov:8080/webgeocalc/#AngularSeparationFinder
we fill out the form as so:





and click the "Calculate" button.

This yields a list of all "full" moons. Scroll down and click on the
"Save All Intervals" button:



We now want to find the moon's distance at all of the times we just
saved (ie, the times of the "full" moons). To do this, start at
http://wgc.jpl.nasa.gov:8080/webgeocalc/#StateVector and fill out as
follows:





NOTE: to get the list of intervals above, drag from the saved
intervals result window into the list of intervals window.

The results, which you can also download, tell you the moon's distance from the Earth at the times of the "full" moons we computed earlier:



I downloaded the results in Excel format, imported them into gnumeric
and sorted by radius (distance from Earth to Moon) and did a little
additional cleanup to get:



(the full spreadsheet is available at https://github.com/barrycarter/bcapps/blob/master/STACK/StateVectorResults.xls)

So, yes, tonight's full moon (yellow) is the closest we'll have until
2034-11-25 (red). It's also the 6th closest moon we'll have this
century.

To see other examples of geocalc in action, see my:


What is the format of the data from the JPL&#39;s HORIZONS system?
https://space.stackexchange.com/questions/18718/calculating-positions-of-moons-ascending-and-descending-nodes-from-ephemeris-fi


For more about how NASA calculates these values in the first place: Where can I find a set of data of the initial conditions of our solar system? which is also now linked to the general "how to compute positions" wiki answer: Where can I find/visualize planets/stars/moons/etc positions?