# Galilean invariance and kinetic energy

## Main Question or Discussion Point

I tried to look this up on the internet. I know there is a book about it but I forgot its title.

I know that you can prove that the kinetic energy should be proportional to velocity squared by saying that this is the only Galilean invariant definition of kinetic energy.

Can someone help me remember how this is defined? (Or maybe better, give the title of the book? I would like to read it!)

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Are you referring to Landau and Lifgarbagez Classical Mechanics? This is the only book I know of where that argument is given, within the first few pages even. But before you go to the trouble of finding the book, is this the argument you are talking about: https://www.physicsforums.com/showpost.php?p=4380393&postcount=9?
That will have to do if I cannot find anything else. But from what I remember the book had a single author and the argument was easier to follow. I translated it into something that a 15-year old could understand.

I don't quite follow the Lagrangian argument myself actually and why you can't choose it to depend linearly on the speed. (I never took the Lagrangian mechanics course because of studies abroad.)

WannabeNewton