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\frac{\partial F(y,y')}{\partial y}-\frac{d}{dx}(\frac{\partial F(y,y')}{\partial y'})=0\\
\frac{1}{y'}\frac{dF}{dx}-\frac{1}{y'}\frac{\partial F}{\partial y'}\frac{dy'}{dx}-\frac{d}{dx}(\frac{\partial F}{\partial y'})=0\\
\frac{1}{dx}(F-y'\frac{\partial F}{\partial y'})=0\\
\frac{1}{\sqrt{2gy(1+y'^2)}}=C(const.)\\
y(1+y'^2)=\frac{1}{2gC^2}
T[y]=\int^{400km}_{0km}\sqrt{\frac{1+y'^2}{2gy}}dx\\
=\int^{2\pi}_{0}\sqrt{\frac{1+(\frac{dy}{d\theta}/\frac{dx}{d\theta})^2}{2gy(\theta)}}\frac{dx}{d\theta}d\theta\\
=\sqrt{\frac{A}{g}}2\pi
x=A(\theta-\sin{\theta})\\
y=A(1-\cos{\theta})
|(t_n - t_{n-1})/(t_n - t_1)|<\delta
|t_n - t_{n-1}|<|Ave|