time-independent

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1: 22.19 Physical Applications

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Figure 22.19.1: Jacobi’s amplitude function $\mathrm{am}(x,k)$ for $0\le x\le 10\pi$ and $k=0.5,0.9999,1.0001,2$. …As $k\to 1-$, plateaus are seen as the motion approaches the separatrix where $\theta =n\pi$, $n=\pm 1,\pm 2,\mathrm{\dots }$, at which points the motion is time independent for $k=1$. … Magnify

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