B757-200 DIVERTS TO ANOTHER ARPT FOLLOWING FAILURE OF LEFT IDG SHORTLY AFTER TKOF.

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ON TKOF ROLL; THE L GENERATOR DRIVE EICAS MESSAGE ILLUMINATED. THE CAPT ELECTED TO CONTINUE THE TKOF ROLL. ONCE WE WERE COMFORTABLE IN THE CLB THE CAPT PROCEEDED WITH THE INFLT CHKLIST. THE CHKLIST HAD US DISCONNECT THE L IDG. PRIOR TO THE DISCONNECT; THE CAPT CALLED DISPATCH AND CONFERRED WITH MAINT AND THE DISPATCHER TO DETERMINE THE BEST COURSE OF ACTION. MAINT HAD US CONTINUE THE CHKLIST WHICH THE CAPT ACCOMPLISHED. PRIOR TO DISCONNECT; I ADVISED THE CAPT THAT I HAD ENCOUNTERED THIS SAME SITUATION IN THE PAST. WE ENCOUNTERED A STRONG JOLT UPON DISCONNECT. AFTER CONFERRING WITH MAINT AND INSTRUCTORS THEY ADVISED ME THAT WE MORE THAN LIKELY HAD SHEARED THE SHAFT OF THE IDG. UPON DISCONNECT; WE ENCOUNTERED THE SAME STRONG JOLT THROUGHOUT THE ACFT AND AS A RESULT WE MONITORED THE SITUATION CAREFULLY AND DECIDED WE NEEDED TO DIVERT. IN ADDITION; DISPATCH ADVISED US THAT WE WERE NO LONGER LEGAL TO ENTER ETOPS AIRSPACE AND THAT WE SHOULD PROCEED TO ZZZ. THE CAPT TRIED TO COMMUNICATE WITH DEP BUT DUE TO ATC'S WORKLOAD HE WAS UNABLE TO TALK TO US. AS A RESULT; THE CAPT DECIDED TO DECLARE AN EMER SO WE WOULD GET PRIORITY HANDLING. WE PROCEEDED TO ZZZ AND LANDED OVERWT. LANDED WITHOUT ANY FURTHER PROB.