[Cleonis]

Hi, I want to respond to a post from you from 2019. (That 2019 thread no longer offers the reply button, otherwise I would reply there of course.) I apologize for using this thread to get my message in.

This is the item I want to respond to: https://news.ycombinator.com/item?id=19768492 When you took a Classical Mechanics course you were puzzled by the form of the Lagrangian: L = T - V

I have created a resource for the purpose of making application of calculus of variations in mechanics transparent. As part of that the form of the Lagrangian L=T-V is explained.

http://cleonis.nl/physics/phys256/calculus_variations.php

http://cleonis.nl/physics/phys256/energy_position_equation.p...

I recognize the 'you are certainly entitled to ask why' quote, it's from the book 'Classical Mechanics' by John Taylor.

Here's the thing: there is a good answer to the 'why' question. Once you know that answer things become transparent, and any wall is gone.

[dataflow]

Haha wow, this was definitely random. Thank you for letting me know, I'll take a look when I have the chance.

[Cleonis]

If I don't hear back in a week or so I will remind you, I hope that's OK with you.

I'm aware your expectations may be low. Your thinking may be: if textbook authors such as John Taylor don't know the why, then why would some random dude know?

The thing is: this is the age of search machines on the internet; it's mindblowing how searcheable information is. I've combed, I got to put pieces of information together that hadn't been put together before, and things started rolling.

I'm stoked; that's why I'm reaching out to people.

I came across the ycombinator thread following up something that Jess Riedel had written.

[dataflow]

Some feedback (apologies in advance for it being negative):

- I mean this kindly, but this is getting a tad bit aggressive. Please let me glance at my own pace (or not glance, if I don't find the interest to), rather than periodically following up with me around the forum to make sure I look at what you wrote. I was much more interested in this problem at the time I came across it than I was in 2019, and I was similarly more interested in 2019 than I am now. During this time I have both (a) come across other explanations that I've found ~semi-satisfactory, and (b) gathered other things to occupy my brain with. While I do get some enjoyment from the topic, refreshing my understanding of analytical mechanics is really not my topmost interest or priority right now. It could easily be months or years before I become interested in the problem again to even think about it.

- I find it rather... jarring to see a sentence like "Summing bars of signed area, in the limit of subdividing into infinitely many bars: that is evaluating the integral" in the middle of an explanation about Lagrangians and the principle of stationary action. Yes... integration is the limit of addition; you should hope your reader knows that well by now. You wouldn't re-teach "multiplication is really just repeated addition" in the middle of a lecture about Fourier series; this feels equally out-of-place. Not only does it make it seem like you don't know your audience, it also wastes the reader's time, and makes it hard for them to find any gems you might have shared.

- I took a quick look at your site and I don't actually see you attempt to explain the rationale for why the quantity of interest is T - V (as opposed to, say, T + V) anywhere. You mention "you are looking for the sweet spot: the point where as the object is moving the rate of change of kinetic energy matches the rate of change of potential energy", but... am I? Really? I certainly wasn't looking for that, nor have any idea why you thought I would be looking for that. It almost seems to assume what you were trying to prove!

[Cleonis]

Thank you for taking the time to have a look.

About the presentation: I think I agree: once I'm up to the level of discussing Lagrangians and stationary action I should not re-teach integration; the reader will be familiar with that.

That particular presentation grew over time; I agree it is uneven. I need to scrap a lot of it.

The preceding article http://cleonis.nl/physics/phys256/calculus_variations.php Is more an overarching concept.

Also, I'm active on the stackexchange physics forum. Over the years: Hamilton's stationary action is a recurring question subject. Some weeks ago I went back to the first time a stationary action question was posted, submitting an answer. In that answer: I aimed to work the exposition down to a minimum, presenting a continuous arch. https://physics.stackexchange.com/a/821469/17198

three sections:

1. Work-Energy theorem

2. The central equation of the work 'Mécanique Analytique' by Joseph Louis Lagrange (I discuss _why_ that equation obtains.)

3. Hamilton's stationary action

It's a tricky situation. I'm not assuming the thing I present derivation of, but I can see how it may appear that way.