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,…
Indeed inertia. Theory of motion consists of describing the properties of Inertia. In terms of Newtonian mechanics the members of the equivalence class of inertial coordinate systems are related by Galilean…
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…
I have created a demonstration of Hamilton's stationary action with interactive diagrams, (supported with discussion of the mathematics that is involved). Interestingly: it is possible to go in all forward steps from…
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 a resource that I think addresses your dissatisfaction. The information is available on physics.stackexchange https://physics.stackexchange.com/a/670705 I use 'Hamilton's stationary action' to refer to…
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.…
I have a hard copy of the first edition. The dedication says: "dedicated to the principle of least action" I have an educational resource for introduction to Hamilton's stationary action. The title is "Least action…
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,…
Indeed inertia. Theory of motion consists of describing the properties of Inertia. In terms of Newtonian mechanics the members of the equivalence class of inertial coordinate systems are related by Galilean…
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…
I have created a demonstration of Hamilton's stationary action with interactive diagrams, (supported with discussion of the mathematics that is involved). Interestingly: it is possible to go in all forward steps from…
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 a resource that I think addresses your dissatisfaction. The information is available on physics.stackexchange https://physics.stackexchange.com/a/670705 I use 'Hamilton's stationary action' to refer to…
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.…
I have a hard copy of the first edition. The dedication says: "dedicated to the principle of least action" I have an educational resource for introduction to Hamilton's stationary action. The title is "Least action…