Lectures on integral invariants and Hamiltonian equations

[wrobel]

I have no idea where to place this post. Just to share my teaching experience . This is a part of my lectures notes. The aim of the text is to present a successive exposition of several pieces of mathematical physics that have common origin. Perhaps it would be of some use for those who teach classical mechanics.
https://arxiv.org/pdf/2507.02878v4

 

[TensorCalculus]

I have no idea where to place this post. Just to share my teaching experience . This is a part of my lectures notes. The aim of the text is to present a successive exposition of several pieces of mathematical physics that have common origin. Perhaps it would be of some use for those who teach classical mechanics.
https://arxiv.org/pdf/2507.02878v4

oh, awesome! Where in a classical mechanics course would you learn this, out of curiosity? Maybe one day I will have the physics skills to properly appreciate the notes... but when would this be is what I am wondering.

 

[Haborix]

oh, awesome! Where in a classical mechanics course would you learn this, out of curiosity? Maybe one day I will have the physics skills to properly appreciate the notes... but when would this be is what I am wondering.

I would say many (most?) people could go through graduate physics studies and not see classical mechanics formulated in the language of differential forms (as used in these notes). But you would still get a taste for the same ideas in an upper-division undergraduate course and graduate course. You'll have to come across professors more mathematically inclined, or take a mathematical physics class of some kind, if you want to see something similar to wrobel's notes.

 

[TensorCalculus]

I would say many (most?) people could go through graduate physics studies and not see classical mechanics formulated in the language of differential forms (as used in these notes). But you would still get a taste for the same ideas in an upper-division undergraduate course and graduate course. You'll have to come across professors more mathematically inclined, or take a mathematical physics class of some kind, if you want to see something similar to wrobel's notes.

ah, so graduate physics + beyond. Not something I would come across soon. But the notes look very interesting - from a quick glance I agree that they are a very mathematical approach to mechanics (not that I can claim to understand much)

 

[gleem]

ah, so graduate physics + beyond. Not something I would come across soon.

Yes, you will have a lot of water under your bridge before you can fully appreciate the article.

 

[felixeli7]

Thanks for sharing! This looks like a thoughtful way to connect different topics in mathematical physics. I'm sure it’ll be helpful for others teaching or studying classical mechanics.

 

[TensorCalculus]

Yes, you will have a lot of water under your bridge before you can fully appreciate the article.


View attachment 363633

Indeed.
My goal: get there before the end of the 2027 academic year

 

[gleem]

My goal: get there before the end of the 2027 academic year

To get where?

 

[TensorCalculus]

To get where?

To a point at which I have the sufficient prerequisite maths and physics knowledge/experience to be able to fully appreciate the paper linked to in post #1

 

[gleem]

My goal: get there before the end of the 2027 academic year

Will not happen, But, if by some chance you think you do, please let us know.

 

[weirdoguy]

Will not happen

Why? I specialize in differential geometric methods in physics, and these notes look like something I attended around 3rd or 4th year of studying. If you study theoretical physics you have to learn fast.

 

[gleem]

Why? I

The OP is a sophomore in HS and has a goal of understanding the paper in two years.

 

[TensorCalculus]

The OP is a sophomore in HS and has a goal of understanding the paper in two years.

Yeah exactly - I'm a 14 year old kid (will not happen is the answer I was expecting, but it never hurts to hope)...
My physics might be good, but it's not that good.... only as good as a maybe 1st-2nd year uni student... being optimistic

 

[weirdoguy]

The OP is a sophomore in HS

Oh lol, I thought OP was another user, sorry. So yeah, @TensorCalculus give yourself 8-10 years.

 

[TensorCalculus]

Oh lol, I thought OP was another user, sorry. So yeah, @TensorCalculus give yourself 8-10 years.

Awww :(
Oh well, worth hoping.

EDIT: Don't worry, I'm already slowly working my way towards that point - forgot about the book in my hand

 

[gleem]

Oh well, worth hoping.

No hoping, only doing.

 

[TensorCalculus]

No hoping, only doing.

Good correction.