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Apr 30, 2018 at 9:12 comment added GerritvdS After reading it, I reread the book on p. 143. There it says "Without a gravitational field, if you rotate the whole system about the origin, nothing changes." Indeed, the lagrangian does not depend on theta. If you look at the figure at the top of this page, you can easily see that a change in theta would leave the system unchanged, whereas a change in alpha would make a difference. Further, the book states that there is "conservation of angular momentum", and not "conservation of total angular momentum". In short, I agree with you now, thanks again.
Apr 16, 2018 at 16:11 review Late answers
Apr 16, 2018 at 16:51
Apr 16, 2018 at 15:55 history answered user191106 CC BY-SA 3.0