Final project ideas using Noether's theorem in simulation class

[hj-hn-hs]

TL;DR Summary: trying to figure out a final project idea that uses noether's theorem in my scientific computing class. i'm an undergrad about to graduate with a ba in physics.

i learned about noether's theorem a year or so ago but haven't had the chance to really sit with it and understand it, let alone try to apply the math. which leads me to now, i have 5 weeks left of my physics scientific computing class and the final project requires c++ for solving the problem(s) and python for visualizing the final system with the necessary research/math/problem solving behind it. i borrowed "emmy noether's wonderful theorem" by neuenschwander and there are lots of problems at the end of each chapter but i'm having a hard time coming up with a project idea, let alone fleshing it out with details to bring to my professor. so far if it helps, we have solved laplaces equation for a parallel-plate capacitor and modeled a damped harmonic oscillator.

 

[fresh_42]

We have an example here in the July 2018 file (the centenary of the theorem) with the solution
https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/
I'm not sure whether this helps, but you could have a look. The theorem itself is not easy stuff.

 

[pbuk]

i borrowed "emmy noether's wonderful theorem" by neuenschwander and there are lots of problems at the end of each chapter but i'm having a hard time coming up with a project idea, let alone fleshing it out with details to bring to my professor.

Noether's theorem is elegant but I can't see how it can povide the basis for a computational project at this level.

i have 5 weeks left of my physics scientific computing class

That's not long.

and the final project requires c++ for solving the problem(s)

So choose something where algorithms can be easily implemented in C++

and python for visualizing the final system

So choose something that has a concrete visualization.

with the necessary research/math/problem solving behind it.

So choose something where either (i) the research/math/problem solving is easy or (ii) you have sufficient natural interest to pursue the research/math/problem solving to its end.

I recommend that you pick something that interests you: music, Formula 1 motorsport, astronomy, football (any kind) statistics, whatever it is there are a number of great projects in there that will get you a good grade if done right.

 

[hj-hn-hs]

Noether's theorem is elegant but I can't see how it can povide the basis for a computational project at this level.



That's not long.



So choose something where algorithms can be easily implemented in C++



So choose something that has a concrete visualization.



So choose something where either (i) the research/math/problem solving is easy or (ii) you have sufficient natural interest to pursue the research/math/problem solving to its end.

I recommend that you pick something that interests you: music, Formula 1 motorsport, astronomy, football (any kind) statistics, whatever it is there are a number of great projects in there that will get you a good grade if done right.

Thank you, I appreciate it!

 

[hj-hn-hs]

We have an example here in the July 2018 file (the centenary of the theorem) with the solution
https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/
I'm not sure whether this helps, but you could have a look. The theorem itself is not easy stuff.

Thank you!