I am convinced that Mechanical Engineers developed their mathematics on another planet. The above figure illustrates the three eigenvalues of a 3x3 matrix. [From Continuum Mechanics for Engineers by Mase and Mase.]
It has something to do with the determination of the magnitude of stress in an arbitrary direction. You compute the stress principals, which are the magnitudes of stress in the directions in which they're largest. Then there's some kind of relationship amongst them that lends itself to graphical representation as a circle.
I don't remember exactly how it works (it *has* been 7 years, although I *am* TAing this class this semester, so I will probably learn...) but you have to keep in mind that stress is represented mathematically as a tensor, and in the age of slide-rules and logarithmic multiplication, having a graphical method to simply *measure* the magnitude of stress was extremely valuable.
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Mohr's Circle
I don't remember exactly how it works (it *has* been 7 years, although I *am* TAing this class this semester, so I will probably learn...) but you have to keep in mind that stress is represented mathematically as a tensor, and in the age of slide-rules and logarithmic multiplication, having a graphical method to simply *measure* the magnitude of stress was extremely valuable.