I was the lead installer for a rather large government installation where some of the projectors we used are the PTD 7700U-K. I have been very unsatisfied with their performance. I have gotten the "shake" you describe from multiple projectors. I have the projectors configured to blend and they are being fed by a Vista Spyder processor. It is almost impossible to keep one projector aligned and blended to another projector. I have worked with Panasonic for many months to resolve the issue and have gone through several different projectors. Panasonic finally sent me a "Matched Set" of projectors that, after they have armed up for about an hour, will not shake and "only" shift one pixel up and one pixel to the right.
We also have a bunch of the 10000 series and we have had some problems with them but not as bad as the 7700 series. The problem was originally blamed on the installation (as usual) but after removing the projectors and placing them on the ground, they still flickered. After that the "blame" was shifted to the power being "unstable" (not a true 60Hz). I called the electric company and found out what area of town was on a separate power grid, did a test on that grid (with the projector sitting, feet down, on concrete) and it still shook. Panasonic asked us to describe the "flicker" and I gave them all the info about the anomaly.
After a couple of months they accepted the fact that yes, indeed, the projectors image shook (flickered).
They sent out replacements and we installed them. One of the "new" projectors flickered. I called them back and they were now convinced that it had to be the installation and brand new projectors would not do that. I did the same tests I did previously. Same results. At that point the went through the trouble of testing 2 projectors at their shop and finding "matched" projectors to send us. I have since reinstalled the matched projectors and have not had any problems with the image shaking from the units.
During the middle of this ordeal, I was at the Infocomm trade show and got the opportunity to speak, face to face, with the customer service reps, sales reps, and engineers that I had been on the phone with. All of the representatives were very helpful and eager to fix the problem, especially when I wanted to discuss the problem in front and center of their publicity booth. After that it was a little easier to get assistance with the problems and after that is, coincidentally, when they went through the trouble of testing in house.
I don't think the Panasonic products are bad quality, but I do think they have some problems with that model.
If your projector is under warranty, call for an RMA and have it replaced. If it is out of warranty.....try to sell it to a bar or club....some place where the building shakes from loud music and no one will notice.