I was recently told that for parts of the Lunar Module's ascent from the surface of the Moon to its rendezvous in orbit, its thrust vector was not in line with its center of gravity, and actually offset due to propellant slosh. This sounds quite scary, since it would give the module a tendency to yaw/spin about an axis, which would require immediate attention from the attitude control system. As such, I was wondering if anyone had any more information on this interesting story, or any papers on the LM that took thrust offset into account during its design. It would be nice to see how far the thrust vector was offset from the CoG, since it might not have posed too much of a problem if the offset was only small. Any info would be much appreciated, thank you!
LM ascent flight control authority was provided by the reaction control system jets. The fact that the ascent engine was non-gimbaling was, of course, planned for. From here:
LM Ascent Powered Flight Control
The LM ascent powered flight autopilot obtains control torque only by means of the reaction jets. The engine is fixed; it cannot swivel. This control, then, operates very similarly to the free-fall coasting flight autopilots described above, but with the addition that the system estimates the torque arising from the offset of the main engine thrust from the center of gravity. Controlled limit cycles then will normally operate so that, unless error margins are exceeded, reaction jets will be fired only to oppose the main engine thrust misalignment.
The LM Handbook states "The engine is installed in the midsection of the ascent stage; it is canted so that the center line is tilted 1. 5° from the X-axis, in the + Z-direction."
Two of the reaction control jet clusters are circled in red on this image.
Just an addendum to Organic Marble's answer: apparently the corrections from the RCS thrusters were very noticeable for the LM crew. While Apollo 10 didn't land the LM, they did separate the ascent stage and test the ascent program; here's an excerpt from the transcript (bolds mine):
110:47:48 Stafford: Yes. Also, just a couple of more comments. It was a real ride, that ascent engine was; I guess we had the longest burn on it to date, and it takes you on quite a little pitch and yaw excursion there as you take off. I mean it continues on, you know, the way, just - with a non-gimballing engine, but yet it burned out beautifully on residuals, but you're really hiccupping back and forth in that bear. It was quite a ride for 15 seconds. Over.
110:48:11 Engle: Roger. I'll bet. I'll bet it got pretty sporty there towards - You had a pretty light vehicle there, didn't you?
110:48:19 Stafford: Oh, yes. Just one pulse in PGNS [Primary Guidance and Navigation System], you go bang, and it really takes off. Also, the vehicle's so light that you noticed all the structure shaking when you fired pulse. And it sounded just like you'd awake inside of a rainwater tub with somebody beating on it with a bongo drum.
110:48:38 Engle: (Laughter) Is that right?
110:48:43 Stafford: Yes, It's quite a machine.
On this occasion, there was some anomaly right at staging that led to a brief loss of control -- I think that's the "quite a little pitch and yaw excursion" referred to.