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The Apollo 13 air to ground voice transcription can be found here:
http://www.jsc.nasa.gov/history/mission_trans/mission_transcripts.htm

The emergency technique that used the Earth and Sun to establish a known
attitude is described on this page:

http://www.universetoday.com/62763/13-things-that-saved-apollo-13-part-6-navigating-by-earths-terminator/

The link to the "navigation report" didn't work for me. I got only a
partial file. But the report is also available here:

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20090026451_2009026278.pdf

"Gimbal lock" is frequently mentioned in the report. Because the
inertial measurement unit's gyro and accelerometer platform was
supported by only three gimbals, there were forbidden attitudes where it
was unable to maintain a fixed orientation independent of spacecraft motion.

Grumman, the Lunar Module contractor, had insisted on four gimbals to
assure total freedom of maneuver. But the designer of the navigation
system, MIT, said that wasn't necessary. A system with three gimbals
would have a size, weight, and reliability advantage.

As recounted in "Digital Apollo" (David A. Mindell, 2008), in early 1964
NASA got both parties together in a meeting and demanded the issue be
explored until one side admitted defeat. MIT came very well prepared and
the decision was for three gimbals. But when Apollo began flying,
everyone soon realized Grumman had been right. The requirement to avoid
gimbal lock imposed an irritating workload on mission control and the
astronauts. Sometimes winning an argument merely proves you're the more
skillful arguer.

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