Question

I'm trying to find the field lines, x, of F(x,y,z)=(y-z,-x,x-y). Am I supposed to use the formula:\[\dot{\underline{x}}=\lambda(\underline{x})\underline{F}(\underline{x})\] for some scalarfield lambda? How does it work?

Answer 1

oh it's F(x,y,z)=(y-z,z-x,x-y)

Answer 2

\[\dot{\underline{x}}=\frac{d\underline{x}}{dt}\]by the way

Answer 3

Seems like some kind of method for graphing curl or divergence, something like that but I don't recognize the formula...

Answer 4

i think it needs more clarification ...

Answer 5

OK, see if he comes back....

Answer 6

looks like some sort of differential equation exercise perhaps ...

Answer 7

Field lines sounds like some sort of contour graph...

Answer 8

or force field jargon ... the closest thing I can come to online is:

http://www.physicsforums.com/showthread.php?t=304499

Answer 9

Ok, that's a set of calculations, normally interpreting curl,div etc graphically is something of a pain, I would be quite interested if there was some better way of doing that....

Answer 10

Of course I should have checked Wiki, doesn't explain the formula though...

This article is about the modern use of "field lines" as a way to depict electromagnetic and other vector fields.

"Modern" , that's why I don't know it, lol.

Answer 11

http://en.wikipedia.org/wiki/Fieldline

Forgot the link...

Answer 12

\[\dot{\underline{r}}(t)=(\frac{dx(t)}{dt},\frac{dy(t)}{dt},\frac{dz(t)}{dt})\]
So you get a system of linear equations. lambda(x) doesn't have an effect on the direction so you can choose anything you want for that I believe.

The answer to this question is supposedly \[x^{2}+y^{2}+z^{2}=c_{1} \]\[x+y+z=c_{2}\] so you get circles.

Answer 13

The line underneath letters means that they're vectors.

Answer 14

Yes, I got that, I will have another look at this a bit later on...

Answer 15

Did I say linear equations, I meant differential equations.