- #1

Happiness

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In the next paragraph, in the second sentence, it wrote "at points ##u=\pm1##, ##f(u)## is always negative, except for the unusual case where ##u=\pm1## is a root". But LHS of (5.62') ##=\dot{u}^2=\dot{\theta}^2\sin^2\theta=0## when ##u=\cos\theta=\pm1##,i.e., ##\theta=0## or ##\pi##. Thus RHS should also be 0. That means ##u=\pm1## is always a root to ##f(u)=0##. What's wrong?