Mohr's circle and formula for eigenvectors

[Bruno Tolentino]

Don't exist formula for the eigenvectors, all right!? Eigenvectors needs be found manually, correct!?
But and about the Mohr's circle? This physical/mathematical theory don't define clearly the direction of the eigenvectors (called principal direction) with the eigenvalues (called principal stress)?

https://en.wikipedia.org/wiki/Mohr'...a_general_three-dimensional_state_of_stresses

 

[jasonRF]

Despite your four question marks, I'm not sure what you are asking here. There are certainly formulas for eigenvalues of low-dimensional (2x2,3x3 or 4x4) matrices, for example:
http://math.harvard.edu/archive/21b_fall_04/exhibits/2dmatrices/index.html
which also has formulas for eigenvectors.
There cannot be formulas for higher dimensional (>4) matrices as there does not exist formulas for the roots of polynomials of order >4.

Hopefully someone that knows something about Mohr's circle can chime in about your 3rd and 4th questions ... to me it looks like an interesting (and probably very useful) graphical technique that is used by mechanical engineers.

jason

 

[Bruno Tolentino]

But, this article doesn't affirm nothing about the general case, when b and c are not zero...

 

[jasonRF]

I think you need to do your algebra again - did you even do the algebra yourself? The link does indeed cover the case where b and c are not zero.

I am confused. Are you trying to claim that Mohr's circle somehow violates what mathematicians claim to be true?

jason

 

[Bruno Tolentino]

I'm autodidact... In my country doesn't exist good teachers and good books... The Mohr's theory and the eigenvectors theory are concept not very clear for me...