00075___7cbfa111e025bce6dc011124fbfcd2b0

00075_7cbfa111e025 - Equation(5 shows that Hence gi characterizes the change of the position vector R as Oi varies In other words gi is directed

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Chap. 2 54 TENSOR ANALYSIS differential that will have a different geometric meaning as will be seen later. By Eqs. (3) and (4), we may write Eq. (1) as where (6) Since g, and gr are linear combinations of unit vectors, they are themselves vectors; they are known as the covariant and contravariant base vectors, respectively, or as the base vectors and reciprocal base vectors.
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Unformatted text preview: Equation (5) shows that Hence gi characterizes the change of the position vector R as Oi varies. In other words, gi is directed tangentially along the coordinate curve @. These vectors are illustrated in Fig. 2.14:2. Fig. 2.14:2. Contravariant and covariant components of a vector v in two dimensions. It is easily verified that...
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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.

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