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Unformatted text preview: The law of transformation of the components of a quantity with respect to coordinate transformation is an important property of that quantity. In the following section, we shall see that a quantity shall be called a tensor if and only if it follows certain specific laws of transformation. All the results above apply as well to the plane (a two-dimensional Euclidean space), as can be easily verified by changing the range of all indices to 1, 2. P R O B L E M S 2.3. Find the components of the Euclidean metric tensor in plane polar coordinates (0, = r,& = 8; see Fig. P2.3) and the corresponding expression for the length of a line element Ans. Let z1,22 be a set of rectangular Cartesian coordinates....
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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