00071___de387d21224c88243c9ea6d3e8e74aba - 50 T ENSOR...

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50 TENSOR ANALYSIS Chap. 2 all coordinate systems which can be obtained by admissible transformations. Since the sum and difference of tensor fields of a given type are tensors of the same type, we deduce that ij a tensor equation can be established in one coordinate system, then it must hold for all coordinate systems obtained by admissible transformations. The last statement affords a powerful method for establishing equations in mathematical physics. For example, if a certain tensor relationship can be shown to be true in rectangular Cartesian coordinates, then it is also true in general curvilinear coordinates in Euclidean space. Thus, once an equa- tion is established in rectangular Cartesian coordinates, the corresponding equation (stating a physical fact, such as a condition of equilibrium, of con- servation of energy, etc.) in any specific curvilinear coordinates in Euclidean space can be obtained by a straightforward “translation” in the language of tensors. The key word here is “tensor.” Every term in the equation must
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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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