OK, I long ago read "Seed of Light" by Edmund Cooper.
Also Heinlein's "Orphans in the Sky".
And am awaiting delivery of Clarke's "Rendezvous with Rama".
Here is a cite, or shortcut, to one of the very first generation ship
stories.
http://amazingstoriesmag.com/articles/voyage-lasted-600-years/
Don Wilcox's "The Voyage that Lasted 600 Years"
( Amazing , October 1940) was the first of dozens of
generation-ship stories,