I'm aware of the phenomenon of push stearing, that the bike wants to keep going straight and therefore leans yada yada yada...

But from a science side of things, does anyone know the physics behind it?

One (hopefully) useful link:

Counter-steering[/list:u]

The basic force that keeps a bike and a motorcycle up is precession; the resistance of a gyroscope to movement of its axis.  That's what keeps gyroscopes up, and it's a force that increases with rotation speed (which is why bikes are so much more stable at speed than at a crawl).  It's fundamentally an inertial force.

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oohhhh..... so sorry... I was reading that article posted by Kerry and must have fallen asleep.... (cleans drool off key board)...

Gyroscopic force is the biggest factor.  Also, try walking a bicycle.  Turn the wheel to the right or left and walk it a step and then bring it back straight.  You'll notice that the bike is now leaning in the opposite direction from the turn.  Throw in gyro effect, and speed and wahlah.  

Now if you're walking the bike and leaning it over, you'll notice that the only way to keep the bike leaning is by pushing out on the handlebars.  The second you pull in on the handlebars you'll walk the bike right up.

I think the gyroscope effect gets more credit than it's due when it comes to balancing a bike.  In fact I'm pretty much convinced it's got nearly nothing to do with it.  I'm pretty sure the front suspension and steering geometry is entirely responsible for the way a bike balances and steers.  This straight dope column discusses it: http://www.straightdope.com/mailbag/mbicycle.html  

Think about it: at low speeds, like 2 mph, balancing a bike is quite easy yet there is no appreciable gyro effect because the wheels are rotating slowly.  Roadstergal is right that a bike at higher speeds feels more stable, I guess this could be due to the gyro effect, but maybe it's just the same front end geometry thing working even more because of the higher speeds?  Not sure.

jeff

Okay....

The posted experiment had to do with bicycles, so I have to wonder how the principles will change considering the weight, size and angular velcoity of the motorcycle wheels.  

And in the article posted by Kerry, it actually does account for rake and trail.