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[maniacal laugh]HAHAHAHA!!!![/maniacal laugh] I figured out how to make C&C tolerable!!!
- Thread starter KillahBee
- Start date
KillahBee
New member
samoth said:Here's an interesting thread about lie derivatives:
http://www.physicsforums.com/showthread.php?t=166053
Vectors to a surface/manifold lie in the tangent spaces to the surface. Each tangent space is a vector space with the same dimension as the manifold(most of the time), and you can add and subtract vectors etc without leaving this tangent space.
However, what happens if you take the derivative of a vector field on the surface in a direction along the surface. In other words if v is teh vector field and w is the direction, then the rate of change of v in the direction of w is grad w v.
The result of this operation is a vector, but in general, in fact nearly always, this vector will not lie in any tangent space to the manifold. You might say, so what. After all if the manifold is embedded in a higher dimensional space we can still consider such vectors as normal. However, for one reason or another in differential geometry, people prefer not to think of the manifold as being embedded in a higher dimensional space, and instead having intrinsic properties. This point of view runs straight into a problem when it turns out that in general, second derivatives lie "outside" the surface and are no intrinsic.
The Lie derivative offers a way out of this dilemma. As it turns out if you compute grad w v - grad v w.
Then by a great stroke of luck, the final result is always in the tangent space to the manifold. Those terms that point the vector out of the tangent space and into higher dimensional space cancel out and you are left with a vector that lies soley in the tangent space. Hence you have a sort of "intrinsic second derivative" and can once again pretend that the higher dimensional space does not matter/exist (sometimes it in fact really may not exist at all!)
To sum up, the Lie derivatibe is useful for the following two reasons:
1) It is a second derivative
2) It is always in the tangent space
Fuck, someone demod this handjob so I can ignore him
oh shit dude just gettin the little rugrat ready for bed. he wants to watch Taladega nights with me lolKillahBee said:
last night he watched RUDY. said its the best movie he's ever seen. (<~lol)
drinkin me a FRESCA black cherry holy yummy flavor.
what's your weather like out there ?(you LOOOOOOOOOVE the weather chat)
H
heatherrae
Guest
Yes, let us make the sexy time right away!Faizakafez said:
Being listed is a good thing, right? 
KillahBee
New member
Smurfy said:
Rudy is the best movie ever. At lease right after you watch it.
Weather is perfect - just like every other day. Fuggin groundhog day out here.
I'm working. My days for the past 2 months have been - wake up at 5am, work til 2pm, go to gym, come home aorund 5ish, work til 10/11pm. Repeat.
MISERY. I'm close to crackin again
Faizakafez
New member
heatherrae said:
I might have to wait till you pop....
