About the stationary action concept: Yeah, it looks impenetrable, but here's the thing: there is a way of looking at it from just the right angle, and then becomes transparent. Part of the story is this: the actual…
As to understanding Hamilton's stationary action deeply: that is accessible. I have created a resource with interactive diagrams. Move sliders to sweep out variation of a trial trajectory. The diagram shows the…
About transitioning from Classical Mechanics to QM, guided by observations. There is a very interesting approach in the quantum physics book by Eisberg and Resnick, section 5.2 To arrive at the Schrödinger equation…
The rewrite of section 2 of the article is now pushed out to the web page. Repeating the links: Page dedicated to the case of a potential proportional to the cube of the displacement:…
About the article with mathematical treatment: http://cleonis.nl/physics/phys256/energy_position_equation.p... One section of that will be replaced in a day or two: the last part of section 2. I completed a new diagram,…
About d'Alembert's principle. A modern name for it is 'd'Alembert's virtual work'. The modern concept of 'work done' was formulated around 1850 (Eighteen-fifty). That is, we shouldn't assume that back in the days of…
While most authors posit the stationary action concept as a given, it is in fact possible to go from the newtonian formulation to the Lagrangian formulation, and from there to Hamilton's stationary action. That is, the…
I will argue that 'has least action as foundation' does not in itself imply that Lagrangian mechanics is a sparser theory: Here is something that Newtonian mechanics and Lagrangian mechanics have in common: it is…
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…
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…
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…
There is a way of _arriving_ at that subtraction, rather than just throwing it out there. A resource I created: Calculus of Variations as applied in physics: http://cleonis.nl/physics/phys256/calculus_variations.php…
I have created a resource for the purpose of making Hamilton's stationary action transparent. It is possible to go in all forward steps from F=ma to Hamilton's stationary action; that is what I present. The path from…
In retrospect: the earliest recognition of a conserved quantity was Kepler's law of areas. Isaac Newton later showed that Kepler's law of areas is a specific instance of a property that obtains for any central force,…
I have a comment about Lagrangian models. (I'm not commenting on the "All-at-once" angle, that is out of my league.) You assert a contrast, with on one hand (traditional physics) tracking motion step by step, and on the…
I created demonstrations with interactive diagrams. http://cleonis.nl/physics/phys256/calculus_variations.php The following case is used as motivation for developing Calculus of Variations: the shape of a soap film…
About Hamilton's stationary action (which you refer to as 'least action'). I have created an educational resource in which I address the question of how it comes about that F=ma can be recovered from Hamilton's…
Here is one way of looking at it: statistical mechanics introduced the concept of entropy. Years ago, in school, the physics teacher gave the following vivid demonstration: The demonstration involved two beakers,…
Sure enough, the principles of Carnot's thermodynamics and the premises of statistical mechanisc look quite differently. The thing is: since both form the same thermodynamics there must be a connection. I submit: the…
Specifically about the Lagrangian of Classical Mechanics (Hamilton's Action) I have discussed that on physics.stackexchange https://physics.stackexchange.com/a/670705/ The ideas are expressed in diagrams. What is…
It is in fact possible to explain Hamilton's action within the context of classical mechanics. On physics.stackexchange I have discussed that, in an answer posted in oktober 2021. That discussion is illustrated with…
I have created an exposition of Hamilton's stationary action that is visualization based. The visualizations consist of interactive diagrams. Each diagram represents a case where the visitor can sweep out a range of…
You mention stationary action. Interestingly, F=ma and Hamilton's stationary action are mutually derivable. The usual presentation is to show that Hamilton's stationary action implies the newtonian formulation.…
About the stationary action concept: Yeah, it looks impenetrable, but here's the thing: there is a way of looking at it from just the right angle, and then becomes transparent. Part of the story is this: the actual…
As to understanding Hamilton's stationary action deeply: that is accessible. I have created a resource with interactive diagrams. Move sliders to sweep out variation of a trial trajectory. The diagram shows the…
About transitioning from Classical Mechanics to QM, guided by observations. There is a very interesting approach in the quantum physics book by Eisberg and Resnick, section 5.2 To arrive at the Schrödinger equation…
The rewrite of section 2 of the article is now pushed out to the web page. Repeating the links: Page dedicated to the case of a potential proportional to the cube of the displacement:…
About the article with mathematical treatment: http://cleonis.nl/physics/phys256/energy_position_equation.p... One section of that will be replaced in a day or two: the last part of section 2. I completed a new diagram,…
About d'Alembert's principle. A modern name for it is 'd'Alembert's virtual work'. The modern concept of 'work done' was formulated around 1850 (Eighteen-fifty). That is, we shouldn't assume that back in the days of…
While most authors posit the stationary action concept as a given, it is in fact possible to go from the newtonian formulation to the Lagrangian formulation, and from there to Hamilton's stationary action. That is, the…
I will argue that 'has least action as foundation' does not in itself imply that Lagrangian mechanics is a sparser theory: Here is something that Newtonian mechanics and Lagrangian mechanics have in common: it is…
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…
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…
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…
There is a way of _arriving_ at that subtraction, rather than just throwing it out there. A resource I created: Calculus of Variations as applied in physics: http://cleonis.nl/physics/phys256/calculus_variations.php…
I have created a resource for the purpose of making Hamilton's stationary action transparent. It is possible to go in all forward steps from F=ma to Hamilton's stationary action; that is what I present. The path from…
In retrospect: the earliest recognition of a conserved quantity was Kepler's law of areas. Isaac Newton later showed that Kepler's law of areas is a specific instance of a property that obtains for any central force,…
I have a comment about Lagrangian models. (I'm not commenting on the "All-at-once" angle, that is out of my league.) You assert a contrast, with on one hand (traditional physics) tracking motion step by step, and on the…
I created demonstrations with interactive diagrams. http://cleonis.nl/physics/phys256/calculus_variations.php The following case is used as motivation for developing Calculus of Variations: the shape of a soap film…
About Hamilton's stationary action (which you refer to as 'least action'). I have created an educational resource in which I address the question of how it comes about that F=ma can be recovered from Hamilton's…
Here is one way of looking at it: statistical mechanics introduced the concept of entropy. Years ago, in school, the physics teacher gave the following vivid demonstration: The demonstration involved two beakers,…
Sure enough, the principles of Carnot's thermodynamics and the premises of statistical mechanisc look quite differently. The thing is: since both form the same thermodynamics there must be a connection. I submit: the…
Specifically about the Lagrangian of Classical Mechanics (Hamilton's Action) I have discussed that on physics.stackexchange https://physics.stackexchange.com/a/670705/ The ideas are expressed in diagrams. What is…
It is in fact possible to explain Hamilton's action within the context of classical mechanics. On physics.stackexchange I have discussed that, in an answer posted in oktober 2021. That discussion is illustrated with…
I have created an exposition of Hamilton's stationary action that is visualization based. The visualizations consist of interactive diagrams. Each diagram represents a case where the visitor can sweep out a range of…
You mention stationary action. Interestingly, F=ma and Hamilton's stationary action are mutually derivable. The usual presentation is to show that Hamilton's stationary action implies the newtonian formulation.…