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June 9, 2003, 09:37 |
G-Invariance---->urgent help please
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#1 |
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what is the meaning of Galilei Inveriance ?
please help to explain it.... |
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June 9, 2003, 10:19 |
Re: G-Invariance---->urgent help please
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#2 |
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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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June 9, 2003, 10:39 |
Re: G-Invariance---->urgent help please
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#3 |
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the problem it's VERY BasiC PhysicS
thanks Tom |
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June 9, 2003, 12:29 |
Re: G-Invariance---->urgent help please
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#4 |
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Hi,
Can you suggest some literature or book specially for Navier-Stoke equation. Regards |
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June 10, 2003, 04:31 |
Re: G-Invariance---->urgent help please
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#5 |
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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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