How to get the first variation of a complex lagrangian?
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How do I get the first variation for this:
$$ int_C Lleft(z,phi,frac{mathrm{d}phi}{mathrm{d}z}right)mathrm{d}z$$
where:
$$z=x+iy,$$
$$mathrm{d}z=mathrm{d}x+imathrm{d}y,$$
$$phi=f(x,y)+ig(x,y).$$
The integral is a complex line integral and $phi$ is an analytical function.
I'm not sure whether the process is identical to that of real analysis. Is it even possible to get such a variation? Does it even make any sense?
complex-analysis calculus-of-variations
edited Nov 22 at 13:04
amWhy
191k27223438
asked Nov 18 at 13:27
BinaryBurst
356110
add a comment |
up vote
1
down vote
favorite
How do I get the first variation for this:
$$ int_C Lleft(z,phi,frac{mathrm{d}phi}{mathrm{d}z}right)mathrm{d}z$$
where:
$$z=x+iy,$$
$$mathrm{d}z=mathrm{d}x+imathrm{d}y,$$
$$phi=f(x,y)+ig(x,y).$$
The integral is a complex line integral and $phi$ is an analytical function.
I'm not sure whether the process is identical to that of real analysis. Is it even possible to get such a variation? Does it even make any sense?
complex-analysis calculus-of-variations
edited Nov 22 at 13:04
amWhy
191k27223438
asked Nov 18 at 13:27
BinaryBurst
356110
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
How do I get the first variation for this:
$$ int_C Lleft(z,phi,frac{mathrm{d}phi}{mathrm{d}z}right)mathrm{d}z$$
where:
$$z=x+iy,$$
$$mathrm{d}z=mathrm{d}x+imathrm{d}y,$$
$$phi=f(x,y)+ig(x,y).$$
The integral is a complex line integral and $phi$ is an analytical function.
I'm not sure whether the process is identical to that of real analysis. Is it even possible to get such a variation? Does it even make any sense?
complex-analysis calculus-of-variations
edited Nov 22 at 13:04
amWhy
191k27223438
asked Nov 18 at 13:27
BinaryBurst
356110
How do I get the first variation for this:
$$ int_C Lleft(z,phi,frac{mathrm{d}phi}{mathrm{d}z}right)mathrm{d}z$$
where:
$$z=x+iy,$$
$$mathrm{d}z=mathrm{d}x+imathrm{d}y,$$
$$phi=f(x,y)+ig(x,y).$$
The integral is a complex line integral and $phi$ is an analytical function.
I'm not sure whether the process is identical to that of real analysis. Is it even possible to get such a variation? Does it even make any sense?
complex-analysis calculus-of-variations
complex-analysis calculus-of-variations
edited Nov 22 at 13:04
amWhy
191k27223438
asked Nov 18 at 13:27
BinaryBurst
356110
edited Nov 22 at 13:04
amWhy
191k27223438
asked Nov 18 at 13:27
BinaryBurst
356110
edited Nov 22 at 13:04
amWhy
191k27223438
edited Nov 22 at 13:04
amWhy
191k27223438
edited Nov 22 at 13:04
amWhy
191k27223438
191k27223438
asked Nov 18 at 13:27
BinaryBurst
356110
asked Nov 18 at 13:27
BinaryBurst
356110
asked Nov 18 at 13:27
BinaryBurst
356110
356110
add a comment |
add a comment |
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