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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