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Galilean invariance and kinetic energy

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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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