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Jacobi amplitude function am(u,k) (chart)

Calculates a table of the Jacobi amplitude function am(u,k) and draws the chart.

-1≦k≦1

[ initial value u

increment

repetition

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u	am(u,k)

$\normal Jacobi\ amplitude\ am(u,k)\\[10] (1)\ am(u,k)=\phi=F^{-1}(u,k),\hspace{20} |am(u,k)|\le \pi\\ \hspace{25}u=F(\phi,k)={\large\int_{\small 0}^{\hspace{25}\phi}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}}\\[10] (2)\ sn(u,k)=sin(am(u,k))=sin\phi\\ \hspace{25}cn(u,k)=cos(am(u,k))=cos\phi\\ \hspace{25}dn(u,k)=\frac{\partial am(u,k)}{\partial u} \\$

Jacobi amplitude function am(u,k) (chart)

Calculates a table of the Jacobi amplitude function am(u,k) and draws the chart.

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