From the world of motorcycling, a tankslapper can be defined as an undesired oscillation of the forks.
When experiencing a 'tankslapper', the handlebars 'wobble' rapidly from side to side, (sometimes so violently that the rider can no loner maintain grip). In extreme cases, (and provided the steering allows), the oscillation is such that the handlebars will hit the sides of the bikes fuel tank, hence the expression 'tankslapper'.
What causes a tankslapper?
The relationship between a motorcycle's tyres and the road is simple physics. The downward force of the tyre on the road surface is matched by an equal and opposite force as the road pushes back. This is Newton's First Law of Motion.
Now consider what happens when a motorcycle's front wheel leaves the ground temporarily, such as when the rider pops a wheelie or accelerates sufficiently such that full contact of the front tyre with the road surface is lost momentarily. If the wheel is still aligned with the direction of travel when it touches back down there's no problem. In fact, the gyroscopic force created by the rotation of the front wheel tends to ensure this. If, however, the alignment is lost, a tankslapper may happen. Alignment with the direction of travel can be lost if the wheel is turned whilst aloft, (don't touch the front brake!), or the direction of travel changes after the wheel lifts, (e.g. when going round a bend).
The important factor here is the castor angle of the motorcycle's steering, (the angle that the motorcycle's forks make with an imaginary line perpendicular to the ground). The castor effect comes into play when a front wheel that isn't aligned with the direction of travel touches back down. The natural tendency in this case is for the wheel to attempt to align itself once more upon regaining contact. Think about how the castor wheels on a shopping cart work, (a shopping cart has a zero degree castor angle, of course).
The rate of castor compensation is inversely proportional to the castor angle of the motorcycle's steering. In other words, bikes with steep steering geometries, (such as sports bikes), are more prone to rapid steering oscillation than, say, cruisers.
In some cases, over-compensation due to the castor effect happens upon 'touch down' and the wheel turns past the centre. The castor effect will rotate the wheel back the other way and handlebar oscillation begins. Normally, at this point, the rider is gripping on for dear life and trying to provide input into the handlebars to correct the oscillation. This is actually the worst thing to do, as the rider can't react quick enough and will tend to put energy into the oscillation. The best thing to do is relax the arms and let the oscillaton reduce naturally.
How to avoid a tankslapper?
Tankslappers are easily avoided - make sure your front wheel never loses full contact with the ground. Modern motorcycles, with their agressive steering geometry, sticky tyres and powerful engines, conspire against this. It's quite easy for a rider to inadvertently lift the front wheel sufficiently to cause it to 'wobble', especially when pulling away out of a curve, when the direction of travel is changing.
Maybe it's time you considered fitting a steering damper?