Stabilizing the camera is only part of the equation. A rigid mounting is a plus for the camera, but a minus for the tape mechanism.
Vibration can be seen in the video due to the tape vibrating as it goes over the heads. Try this experiment:
Record some smooth video with the recorder not moving. Then rewind and start playing it back. Now start shaking the recorder as if it was getting vibrations through a rigid mount on a racecar. The video will shake as well even though it was recorded smooth. I have tried this on a couple of camcorders including a mini-DV and gotten the same results.
The best idea I have heard so far came from Jon Lowe (914 guru). He hard mounted a cheap mini camera (
www.supercircuits.com) and then ran the output to the input of a camcorder(make sure yours has AV inputs). The camcorder was mounted in a foam lined breadpan on the floor of the car to insulate the tape mechanism from the vibration.
This may also be one of the few times that the extended warranty may be worth the extra money.
Edit: This technique also limits the mass of the camera (thereby increasing the resonant frequency of the system??) as mentioned by IROC. He is a mechanical type and probably has a more complete explanation. Be sure and ask him about fasteners, also.
FWIW,
Rob
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Rob Channell
One Way Motorsports
1979 911SC mostly stock

1972 911T Targa now with a good 2.7

1990 Miata (cheap 'n easy)
1993 C1500 Silverado (parts getter)