Noether's theorem for point particles

[William Crawford]

TL;DR

Literature recommendations for Noether's theorem for point particles.

Hi PF,

As I'm delving back into analytical mechanics, I've noticed that many textbooks don't provide an in-depth discussion of Noether's theorem in the context of point particle Lagrangian mechanics. Does anyone have recommendations for resources (books or otherwise) that cover this topic in detail?

Thanks!

 

[jambaugh]

I believe the reason for this is that one can model point particles as Dirac delta-function distributions. Then the continuum results of Noether's theorem carry over directly.

 

[PeroK]

TL;DR Summary: Literature recommendations for Noether's theorem for point particles.

Hi PF,

As I'm delving back into analytical mechanics, I've noticed that many textbooks don't provide an in-depth discussion of Noether's theorem in the context of point particle Lagrangian mechanics. Does anyone have recommendations for resources (books or otherwise) that cover this topic in detail?

Thanks!

"Emily Noether's Wonderful Theorem" by Dwight Neuenschwander is dedicated to Noether's theorem. I had mixed feelings about it. There were a number of gross errors and I thought the Rund-Trautmann approach was mathematically a bit shaky. That said, I'm not sure there's anything better. Most other textbooks skate through the theorem very quickly.

 

[Haborix]

I'm almost certain it is treated in Arnold's classical mechanics book and Marsden's giant tome, but both of those references are very much on the mathematical side of things. I don't have either at hand to be able to verify.