this is a problem confusing me, which is in the book named Principles of Quantum Mechanics by R. Shankar. This problem is not about quantum mechanics, but just in the chapter of Review of Classical Mechanics. (The ******** is just to avoid to be deleted). The problem is in the attachment, first I have to sorry about my expression in English. Please make it clear that what is canonical transformation(I just know some kind of comprehension in the book, I want your guy's comprehension about Lagrangian and Hamiltonian mathod, the canonical transformations, the symmetries and their consequences) I am here expecting your comprehension and reply to my problem. I didn't study the analytical mechanics, but now we are self-studying the principles of quantum mechanics in the dicussion class! Hence, we do not have a good comprehension about the classical mechanics. But we think it is very important for our further study.