A cycling coach recently told me that I need to reduce my hip rocking while pedaling. He said that it is more efficient to keep your hips steady, rather than allowing them to rock up and down. To me, it feels actually more powerful to allow my hips to rock, rather than forcing them to stay steady.

In trying to understand this from a physics/engineering standpoint, consider this. When you stand up to pedal, as when sprinting, doesn't it feel more powerful to allow the bike to rock back and forth underneath you? Isn't this rocking of the bike the same as a corresponding rocking of the hips while seated?

Here's another thought experiment that is related. If sprinting while allowing the bike to rock results in greater speed (which must be true, since all of the pro sprinters do it), what happens when the bike is mounted in a trainer? With the bike fixed vertically like that, so that you can't allow it to rock, but if you want to generate maximum power, it seems to me that the only way to do so is to allow your hips to rock instead.

Any thoughts?