MIT 3.60 Lec 18b Symmetry, Structure, Tensor Properties of Materials
PROFESSOR: OK, why don't we you get started again? I can understand why there is an air of excitement in the room since tomorrow's a holiday. But we still got two hours before the day is over. Any questions on what we have done up to this point? No, that's good. Let me erase some of this art work then and ask why one would indulge in this rather bizarre exercise of taking the elements of something that represents a physical property and constructing a surface out of them. Well, the name suggests that maybe these surfaces, be they hyperboloids of one or two sheets or imaginary ellipsoids, have something to say about the property that the tensor that formed the coefficient of these functions is doing. So let me take the case of an ellipsoid. That would be the case where all the coefficients are positive. And let's let this be x1 and this x2. And let me ask a first question. If this is to be a well deserved function, does the surface transform in exactly the ...