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Solve the Euler-Lagrange equation

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tandemuse
tandemuse 2021-8-17
关闭： John D'Errico 2021-8-17
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Using calculus of variations (optics subsection) we can show that the following Euler-Lagrange equation must be true:
with the boundary conditions and .
is a matrix of slowness values (inverse of velocity), so for every point in space we know the velocity values. Say for example this is the peaks function:
x = -2:0.05:2;
y = x';
[X,Y] = meshgrid(x,y);
s = peaks(X,Y);
imagesc(s)
xlabel('x')
ylabel('y')
represents the curve we're trying to find, which starts at the point and ends at the point (the boundary conditions).
Find by solving the Euler-Lagrange equation.

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