Ryan Entwistle , Feb 18, 2007; 02:04 a.m.
Shooting in low light conditions with flash, and trying to avoid shadows, you have a few options. Given your constraints, the best one may be as follows:
If there is any usable ambient light at all, you might be able to take a longer exposure so that you have enough ambient light to light the background and use the flash to stop the dog in motion. Ideally, you set the flash to the end-curtain sync of the shutter so that if there is any ambient light exposure trail on moving objects it will "trail behind" the object/subject. (The same technique can also be used to show an object in multiple positions of motion in the same long exposure by using multiple flash bursts, however, this will only work correctly if you can pretty much isolate the flash so that it is not hitting anything but the moving object.) You will need to have the camera on a tripod to keep it steady throughout the log exposure.