Quick vector analysis reminder

make up a vector field with rotation 0.
make up a different one, also with rotation 0.
done.

there's nothing like a quick savvy reply to make you think "well that was stupidly simple" about your question

For the same reason
[math] f(x_0) = 4 [/math]
doesn't determine [math]x_0[/math] for
[math] f(x) := x^2 [/math]

One tells you the magnitude, the other the direction, in a sense.

>>8938814
Helmholtz theorem.

https://en.wikipedia.org/wiki/Helmholtz_decomposition

Also, this >>8938828. If you have a vector field that can be explained only by curl, it has zero divergence. Clearly there are vector fields with non-zero divergence, so at the very least you need more than just curl to define a vector field unambiguously.

File: nasa.png (89KB, 680x520px) Image search: [Google]

89KB, 680x520px

>>8938814
They say that any vector field determined by only the divergence and curl must necessarily preclude longitudinal EM modes that are allowed in the quaternion field theory. Can't confirm though, I haven't derived Maxwell's equations in quaternion formalism yet.

>Doc is a gold mine
>https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050170447.pdf
>specifically sections 3 and 4
>Borderland Sciences
Research Foundation seems like a interesting enterprise

Not fully. You will get a constant C that is yet to be determined.

>>8938837
That's completely unrelated

could somebody tell me how you visualize curl in 3d space? I've got the concepts down but I can't figure out how curl would manifest in 3d

>>8939043

>advanced

>>8939666
Imagine a vector field in 3D, ie: a lot of tiny arrows pointing in some direction that changes continuously. Select some point in the vector field. It has an associated vector. Now rotate point slightly about the origin, say. Does the vector associated with it point in a different direction? If yes, it has non-trivial curl.

>>8938814
Any conservative field will have curl zero, but there's more than one conservative field, so it's not enough to know only one. I don't know a quick proof of why both is sufficient though.

>>8939043
>I haven't derived Maxwell's equations in quaternion formalism yet.
weren't maxwell's equations originally in quaternion notation?

>>8939086
thats completely related