Can Circulation be Computed in a System with an Open Path of Integration?

[Jhenrique]

Exist circulation in a system/circuit/vector field/anything where the path of circulation is open?

Is possible to compute the circulation of a system/circuit/vector field/anything with an open path of integration?

 

[Matterwave]

Do you have a specific mathematical definition of circulation in mind? Usually circulation is defined only for closed paths. If paths are open, one would no longer call it circulation.

 

[Jhenrique]

Do you have a specific mathematical definition of circulation in mind? Usually circulation is defined only for closed paths. If paths are open, one would no longer call it circulation.

Yeah, I have (post #4): https://www.physicsforums.com/showthread.php?p=4768249&posted=1#post4768249

 

[Matterwave]

If that's the definition, then "circulation" the word should only mean for closed paths. Of course you can take a line integral over an open path, that's perfectly well defined, but you just don't call it "circulation".

Are you having trouble with the definition of the word "circulation"? Or is there a math problem you're confused about?

 

[Jhenrique]

If that's the definition, then "circulation" the word should only mean for closed paths. Of course you can take a line integral over an open path, that's perfectly well defined, but you just don't call it "circulation".

Are you having trouble with the definition of the word "circulation"? Or is there a math problem you're confused about?

The surface integral of a vector field over a open surface has name: "flux"
The surface integral of a vector field over a closed surface has name: "flux"

The line integral of a vector field over a closed curve has name: "circulation"
But the line integral of a vector field over a open curve hasn't name...

 

[Matterwave]

Is that a fundamental problem you think? Say you have a straight line integral, would you still like to call this integral "circulation" even though it has nothing to do with anything circular?