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Unformatted text preview: g's and g's follows the tensor transformation law. A substitution of Eq. (16) into Eq. (15) and vice versa yield g~ = pik& = Pikp?grn gm = Pkmgk = P(e,&,'gr , which implies that We can now determine the transformation law for the components of v between different coordinate systems. Dotting both sides of the equation -r- 21 gr = vmgm with gi gives the transformation law (19) A vi = (gi ' g m ) P = p:mu". Similarly, dotting the same equation with gj gives the inverse transforma- tion Using the relations of the contravariant base vectors (21) A g' r= (g" . gm)gm = p&gm, gm = (g, . gm)g' = p;"gT,...
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This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.
- Fall '05