[TriLUG] OT: auto-centered video[1]?

[Brian via TriLUG]

Hi Gang,

I am still in my Monday-morning brain fog and can't figure out good 
search terms to describe the following.

I have seen some YouTube videos which have some sort of processing 
applied which corrects for shaky camera work by constantly moving the 
frame around in a larger area to keep the subject visually still.  It 
has the appearance of constantly-varying letterboxing.

I can't imagine people being patient enough to do this by hand, so there 
must be some software that does it.  I just don't know what to call the 
effect.

Anyway, the point is I have some 350+ photos from last week's eclipse in 
which the image gradually traverses the frame because my celestial 
tracking mount didn't work out (the lens was too heavy for it).  I want 
some easy way to process all the images to center the sun in the frame. 
  Given the very sharp edges involved, it seems like it would be an easy 
target for automation.

Any suggestions?

Thanks,
-Brian

[1] - okay, my use case is a series of stills, but that's what video is 
anyway!