Grandsons of Charlemagne

Could anyone advise me on some books on the subject of Charlemagne's three grandsons, who after Verdun 843, divided the empire. This formative period of Europe interests me very much.

The later Carolingians are not well covered in English, IMHO, but a survey of my shelves turns up "The Carolingian Empire", by Heinrich Fichtenau, and "Carolingian Civilization: A Reader" assembled by Paul Edward Dutton. Historical Fiction usually jumps from Charlemagne to the Vikings, not covering anything in between. The New Cambridge Medieval History, and of course, the older Cambridge Medieval history, have relevant volumes. I admit, as far as slow-motion train wrecks go, the later Carolings are serious contenders.

There's a fair amount of material out there. Unfortunately, though I have about 20 books on the Carolingians I haven't started reading them (stuck on Early Christianity at the moment) so I can't really recommend any.

I happen to have Struggle for Empire: Kingship and Conflict under Louis the German, 817-876 by Eric Goldberg (friggin' hilarious speaker BTW) and I'm sure there are books about Lothar and Charles the Bald.

But a good starting point, though I haven't read it, should be The Carolingian World by Marios Costambeys. The Cambridge Medieval Textbooks are usually pretty good, it isn't too expensive and, as it was published in 2011, it should give you lots of good, recent references you can pick from for further reading.