Cleonis

6 ms·

1.
by Cleonis 3mo ago
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 criterion is: the tr
2.
by Cleonis 9mo ago
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 response. https:/&
3.
by Cleonis 11mo ago
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 Eisberg and Resnick const
4.
by Cleonis 11mo ago
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: http://cleonis.nl/physics/phys256&
5.
by Cleonis 11mo ago
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 di
6.
by Cleonis 11mo ago
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
7.
by Cleonis 11mo ago
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 relations betwee
8.
by Cleonis 2y ago
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 transformation. In terms of relat
9.
by Cleonis 2y ago
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 necessary to spec
10.
by Cleonis 2y ago
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. T
11.
by Cleonis 2y ago
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
12.
by Cleonis 2y ago
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
13.
by Cleonis 2y ago
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.p
14.
by Cleonis 2y ago
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 F=ma to Hamil
15.
by Cleonis 3y ago
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, not just the
16.
by Cleonis 3y ago
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 other
17.
by Cleonis 3y ago
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 fil
18.
by Cleonis 3y ago
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 Newtonian mechan
19.
by Cleonis 3y ago
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 stationar
20.
by Cleonis 3y ago
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, stacked, the openings facin
21.
by Cleonis 3y ago
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 qualification &#x2
22.
by Cleonis 4y ago
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. Wha
23.
by Cleonis 4y ago
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 animated GIF's
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by Cleonis 4y ago
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&#x27
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by Cleonis 4y ago
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 trial trajectories
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by Cleonis 5y ago
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. Interestingly, it i
27.
by Cleonis 6y ago
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 visua