| Topic: |
Science > Physics |
| User: |
"bowo" |
| Date: |
24 Jan 2005 08:38:32 PM |
| Object: |
Please prove Poincare lemma |
Hi,
I'm a Physics student from Indonesia. Could anyone please give me proof
(in detail) of Poincare lemma ("All the exact forms is closed")?
Because
I haven't take Differential Geometry class. But I really interested.
If possible, could anyone also prove in detail that "the inverse of the
statement (Poincare lemma) is true locally, but not globally"?
I really appreciate if you'd like to help me on this problem. I guess
it's not a difficult problem for some of you. :)
Thank you very much.
Best regards,
Firdaus Prabowo
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| User: "Sam Wormley" |
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| Title: Re: Please prove Poincare lemma |
25 Jan 2005 12:02:08 AM |
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bowo wrote:
Could anyone please give me proof (in detail) of Poincare lemma
("All the exact forms is closed")?
Because I haven't take Differential Geometry class.
Is this what you're writing about?
http://mathworld.wolfram.com/PoincaresLemma.html
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| User: "bowo" |
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| Title: Re: Please prove Poincare lemma |
25 Jan 2005 08:23:15 AM |
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yes, that's the Poincare lemma. Is there anyone could show me a detail
proof of it??
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| User: "Sam Wormley" |
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| Title: Re: Please prove Poincare lemma |
25 Jan 2005 08:58:58 AM |
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bowo wrote:
yes, that's the Poincare lemma. Is there anyone could show me a detail
proof of it??
See: http://www.google.com/search?q=+Poincare+Lemma+Proof
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| User: "tj Frazir" |
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| Title: Re: Please prove Poincare lemma |
25 Jan 2005 09:37:46 AM |
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Re: The Most Amazing Discovery of All Times
Group: sci.physics Date: Mon, Jan 24, 2005, 6:47pm From:
GravityPhysics@webtv.net (tj=A0Frazir)
=A0=A0BGR says NOPE.
=A0=A0dark energy is 99.9 % of all the energ that ever exsisted taking
up more space.
=A0=A0=A0=A0The universe expands.
=A0=A0Mass is the sum of the low that forms around mass as the universe
expands.
=A0=A0GravityPhysics=A0
=A0=A0=A0=A0((((((Evrything falls the same speed ,,because evry atom
changes mass in the field at the same rate
=A0=A0now that statement aplys to gravity and EMF. Re: Survey of Minds
Group: sci.physics Date: Sun, Jan 23, 2005, 9:17pm From:
GravityPhysics@webtv.net (tj=A0Frazir)
In any energy slope mass will be displaced at the rate it can change
mass.
=A0=A0The rate an atom can change mass is fixed. as an atom is an energy
slope has more mass on 1/2 the atom than the other. =A0=A0. >>>> but
kenetic energy is mass in motion. As the atom is in motion it takes up
more space per time unit. 1/2 the atom has a larger LOW as it takes up
more space per time unit. The sum of the low is mass.
<<<<
An atom in motion threw energy as it expands is taking up more space as
it moves . Eliminating space ahead and leaving a low behind.,<<<<<
=A0=A0=A0=A0As an atom moves threw one time frame
=A0=A0the streak it leaves in time will afect how much mass is on each
side of the atom and a gain in mass is pushing te other 1/2 of atom .
=A0=A0the distortion or drag of an atom in motion is a low and part of
the sum of te atoms mass.
kenetic energy is related to gravity as they boath deal with the rate an
atom changes mass. <<<<<<
=A0=A0=A0=A0=A0The speed of fall is fixed.
The reason the rock hits the moon instead of the moon and rock moving
twards each other
=A0=A0is kenetic energy .
=A0=A0The energy slope at the serface of the moon is 90 deg . On the
earth
its 90 deg.
=A0=A0a rock falls the same speed on the moon . It wieghs 1/6 but falls
the same speed.
=A0=A0nasa has it wrong.
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| User: "" |
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| Title: Re: Please prove Poincare lemma |
25 Jan 2005 01:41:45 PM |
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bowo wrote:
Hi,
I'm a Physics student from Indonesia. Could anyone please give me
proof
(in detail) of Poincare lemma ("All the exact forms is closed")?
The simplest example: for functions A(x,y), B(x,y) if dA/dy = dB/dx
then define
p(x,y) = integral (x A(sx,sy) + y B(sx,sy)) ds
with the integral taken for s = 0 to 1. The partial of p with respect
to x is found by differentiating inside the integral:
dp/dx = integral (A(sx,sy) + xs dA/dx(sx,sy) + sy dB/dx(sx,sy)) ds
= integral (A(sx,sy) + xs dA/dx(sx,sy) + ys dA/dy(sx,sy)) ds
= integral (A(sx,sy) + s d/ds (A(sx,sy))) ds
= integral d/ds (s A(sx,sy)) ds
= 1 A(1x,1y) - 0 A(0x,0y)
= A(x,y)
with a similar derivation showing dp/dy = B(x,y). This assumes that A,
B and their derivatives are continuous so that differentiation can be
done under the integral sign, and that they are defined at all points
on and near the path { (sx,sy): s ranges from 0 to 1 }, which connects
(0,0) to (x,y).
For the path r(s) = (sx,sy), dr = s (dx,dy). So the integral above is
just:
p(x,y) = integral (A,B).dr.
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| User: "bowo" |
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| Title: Re: Please prove Poincare lemma |
31 Jan 2005 01:21:17 AM |
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I don't think this is the answer I need. I'm sorry, but are you really
know Poincare lemma?
I see it as an explanation about how to prove an exact differential or
integral. Or am I mistaken?
Thank you.
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| User: "bowo" |
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| Title: Re: Please prove Poincare lemma |
31 Jan 2005 02:39:04 AM |
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I don't think this is the answer I need. I'm sorry, but are you really
know Poincare lemma?
I see your writing as an explanation about how to prove an exact
differential or
integral. Or am I mistaken?
Thank you.
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