00071___de387d21224c88243c9ea6d3e8e74aba

# 00071___de387d21224c88243c9ea6d3e8e74aba - 50 T ENSOR...

This preview shows page 1. Sign up to view the full content.

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
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 01/04/2012 for the course ENG 501 taught by Professor Thomson during the Fall '05 term at MIT.

Ask a homework question - tutors are online