You may have noticed that trains have a tendency to move side to side. This has to do with the conical shape of train wheels. They have a slightly smaller diameter on the outside than on the inside, as in this simple diagram. Thus when the wheelset lurches over to one side (the right, say) due to an imperfection in the track, the rail on the right comes under the inner part of the wheel where the diameter is larger. This causes it to roll faster than the other wheel, making the wheelset veer to the left, and the process starts over.
So fast trains have yaw dampers to stop this back-and-forth motion, technically called "hunting". The dampers have a high initial resistance, and the dampening force is constant as the bogie continues to move. That means that the effect is also present when the train is going through a curve.
Data! Increase power to the inertial dampers!
If you've ever heard that phrase on Star Trek, you might have wondered what the inertial dampers really are. Well, since the starships in Star Trek can travel faster than the speed of light, the issue arises of how to not splatter the crew on the rear wall when the ship is accelerating. To make the series a little less unrealistic, the writers gave the ships inertial dampers. Exactly how they work has not been detailed yet, at least not on the TV show.
Now, the yaw dampers on the Acela Express and other fast trains aren't quite as spectacular as the special effects on TV. In fact you don't even notice them, and that's a good thing. But on older or simpler trains, you may have noticed that the train moves side to side, sometimes shaking the heads of fellow passengers in a comical way.
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