# Applications of abstract algebra to engineering

## Main Question or Discussion Point

I was wondering if there are any applications of abstract algebra to engineering and where I can go to learn about them?

Related General Engineering News on Phys.org
First obvious subset of abstract algebra would be vector spaces. But just about every scientific field uses advances from that area. But where it is most used would be CFD and FEA. Also, Electrical Engineering and any engineering to do with controls (namely state space methods).

AlephZero
Homework Helper
There are some applications of group theory to problems with complcated symmetries.

For example, there are vibration patterns of a circular disk supported at the center, with N radial and M cirumferential nodal lines, for any integers N >= 0 and M >= 0. That's simple enough.

Now consider the vibration patterns of something like a fan with K identical blades mounted on a central hub. There are analogous sets vibration patterns, but they are not so obvious because every blade may be vibrating in a different way, for example if there are no common factors between the number of blades and the number of radial "nodal lines".

Now consider the case where these vibration patterns are rotating around the disk as travelling waves, rather than forming a "stationary" vibration pattern"

Now consider the disk is also rotatiing, but not at the same speed as the waves are rotating around it.

And finally couple several of these together one flexible rotor, with different numbers of blades in each disk...

Some general theory of to how to keep track of what is going on is quite useful here

It gets even more interesting when you make the more realistic assumption that the blades are only approximately identical, to within manufacturing tolerances etc.

I suppose it kinda depends on your idea of abstract algebra, by my book includes modular arithmetic.

So in reading this on you miracle of modern engineering - your pc - you are using abstract algebra.

Last edited:
There are some applications of group theory to problems with complcated symmetries.

For example, there are vibration patterns of a circular disk supported at the center, with N radial and M cirumferential nodal lines, for any integers N >= 0 and M >= 0. That's simple enough.

Now consider the vibration patterns of something like a fan with K identical blades mounted on a central hub. There are analogous sets vibration patterns, but they are not so obvious because every blade may be vibrating in a different way, for example if there are no common factors between the number of blades and the number of radial "nodal lines".

Now consider the case where these vibration patterns are rotating around the disk as travelling waves, rather than forming a "stationary" vibration pattern"

Now consider the disk is also rotatiing, but not at the same speed as the waves are rotating around it.

And finally couple several of these together one flexible rotor, with different numbers of blades in each disk...

Some general theory of to how to keep track of what is going on is quite useful here

It gets even more interesting when you make the more realistic assumption that the blades are only approximately identical, to within manufacturing tolerances etc.
I'm not seeing how you could model this using groups.

Mind explaining it a bit more?

Homework Helper
In the book I'm just going through, one of the examples in the exercises is binary coding.