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G-Invariance---->urgent help please

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Old   June 9, 2003, 09:37
Default G-Invariance---->urgent help please
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xiang
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what is the meaning of Galilei Inveriance ?

please help to explain it....
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Old   June 9, 2003, 10:19
Default Re: G-Invariance---->urgent help please
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Tom
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It's an expression of Newtons first law; i.e. the equivalence of inertial frames. This basically means that the equations of motion must be the same in all inertial frames.

If we have two inertial frames one at rest x and another moving at constant velocity c with respect to x, X say, then

X = x - ct

The velocity v measured in frame x is then V=v-c in frame X. The equations of motion in frame X is obtained from that in frame x by replacing x,v with X,V. This is Galilean invariance.

It's VERY basic physics.
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Old   June 9, 2003, 10:39
Default Re: G-Invariance---->urgent help please
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xiang
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the problem it's VERY BasiC PhysicS

thanks Tom
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Old   June 9, 2003, 12:29
Default Re: G-Invariance---->urgent help please
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A.S.
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Hi,

Can you suggest some literature or book specially for Navier-Stoke equation.

Regards
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Old   June 10, 2003, 04:31
Default Re: G-Invariance---->urgent help please
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Tom
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It depends on your background and what you want to know. (I'm a mathematician and so the following are rather biased):

A good basic text is

Elementary fluid dynamics bt David Acheson (Oxford University Press)

An introduction to fluid dynamics by Paterson (Cambridge University Press)

is also a reasonable book. If you have a more physics based background then

An introduction to fluid dynamis by G.K. Batchelor (Cambridge University Press)

is probably a good place to start.

Hydrodynamics by Lamb (Cambridge/Dover?) is also worth a look (although it's pre-tensor analysis) as are

Theoretical hydrodynamics and Theoretical aerodynamics

both by Milne-Thompson and published by Dover.

For more rigorous discussion try

Applied analysis of the Navier-Stokes equations by Doering and Gibbon (Cambridge Unversity Press)

or, if you can find it,

The mathematical theory of incompressible viscous flow by O.A. Ladyzhenskaya

There's also a two volume set by Pierre-Louis Lions (Oxford University Press) but I haven't seen these (yet) and various books by Roger Temam.
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