Mixing
How to get the first variation of a complex lagrangian?
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 '18 at 13:04
amWhy
192k28225439
asked Nov 18 '18 at 13:27
BinaryBurstBinaryBurst
354110
add a comment |
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 '18 at 13:04
amWhy
192k28225439
asked Nov 18 '18 at 13:27
BinaryBurstBinaryBurst
354110
add a comment |
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 '18 at 13:04
amWhy
192k28225439
asked Nov 18 '18 at 13:27
BinaryBurstBinaryBurst
354110
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 '18 at 13:04
amWhy
192k28225439
asked Nov 18 '18 at 13:27
BinaryBurstBinaryBurst
354110
edited Nov 22 '18 at 13:04
amWhy
192k28225439
asked Nov 18 '18 at 13:27
BinaryBurstBinaryBurst
354110
edited Nov 22 '18 at 13:04
amWhy
192k28225439
edited Nov 22 '18 at 13:04
amWhy
192k28225439
edited Nov 22 '18 at 13:04
amWhy
192k28225439
192k28225439
asked Nov 18 '18 at 13:27
BinaryBurstBinaryBurst
354110
asked Nov 18 '18 at 13:27
BinaryBurstBinaryBurst
354110
asked Nov 18 '18 at 13:27
BinaryBurstBinaryBurst
354110
354110
add a comment |
add a comment |
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