# Rotation as an example of symmetry in classical mechanics

I modified the question because it was confused.

On my book there is this mathematical definition of symmetry transformation:

"The equations of motion have a symmetry, if the solutions of the equations transformed by the symmetry are still solutions of the equations of motion, namely, there is a symmetry if the transformed equations of motions have the same form of the original".

I don't understand the meaning of this sentence, do you think is it a good (and easy) mathematical definition of symmetry transformation? Anyway what "equal in form" means? Then, i know rotation of an isolated system is a symmetry, can you make an easy example of an isolated system in which if we apply a rotation the mathematical definition of symmetry apply? Can you make an example of non symmetric transformation and show me why the mathematical definition doesn't apply?

• Which textbook? – Qmechanic Jun 13 '19 at 15:59
• Title “Lezioni di fisica teorica” author: Nino Zanghì page 79. It’s in italian anyway: ge.infn.it/~zanghi/FT/ZUM.pdf – SimoBartz Jun 13 '19 at 16:32