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Unformatted text preview: since the topic is not absolutely necessary for the development of solid me chanics, we shall not discuss it in detail, but merely outline below some of the salient results. We discussed in Sec. 2.3 the metric tensor gij in a set of general coordi nates (xl, x2, z3), and in Sec. 2.6 the associated metric tensor gij. By means of these metric tensors, the Euclidean Christoflel symbols r&(xl, x2, x3) are defined as follows: The Ei = f'(xl, x2, x3) as follows (see Prob. 2.24, p. 55) is not a tensor. It transforms under a coordinate transformation ?P This equation can be solved for d2xX/b%"b%@ by multiplying (2) with bxm/aei and sum over i to obtain (3) Interchanging the roles of xi and Zi and with suitable changes in indices, we can substitute (3) into Eq. (2.11:5) to obtain axx a x p 1 ' a?  ap axp aei aei _ . b P den  r;&) aee axPbe:"bxX...
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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
 Thomson

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