Re:Advances in number theory inspired by physics
by wbl on Saturday December 02, 2017 @10:15AM
(#15832143)
https://en.wikipedia.org/wiki/Christoffel_symbols is probably what you wanted to say
Re:Advances in number theory inspired by physics
by kurthr on Saturday December 02, 2017 @03:18PM
(#15833822)
Lol... german potatoes... autocorrect? Thanks, that's actually hilarious.
Re:Advances in number theory inspired by physics
by mkl on Saturday December 02, 2017 @03:22AM
(#15830899)
> Interestingly, mechanical engineering also deals almost entirely with tensors... and they've developed extremely intuitive visualization tools.
What visualisation tools are you referring to? That sounds interesting.
Re:Advances in number theory inspired by physics
by kurthr on Saturday December 02, 2017 @03:33PM
(#15833893)
Since all 3D stress/strains are tensor quantities (even for purely linear models), MEs project them into principal axes so that you can see their angle and their peak tesnsile/shear stress.
https://en.wikipedia.org/wiki/Cauchy_stress_tensor
Look at Mohr's circle:
https://en.wikipedia.org/wiki/Mohr%27s_circle
Within an object the stresses and strains (and principal components) vary as you move through it. That's part of what makes predicting failures and effects of thermal expansion so complex, etc difficult even ignoring nonlinear effects and failure modes (e.g. crack propagation).
Raising and lowering Kartoffel symbols and their covariant derivative forms make manipulating the coordinate transforms possible (4-6 dimensional)... otherwise it would just look like pages of equations.
Interestingly, mechanical engineering also deals almost entirely with tensors... and they've developed extremely intuitive visualization tools.