I'd like to start with some remarks about the general question of how we categorize our physics concepts into 'fundamental' and 'derivable-from-first-principles'. After that I will go into the stationary action concept specifically.
Two examples:
In the case of refraction of light there was...
As pointed out by contributor Orodruin, the content of Hamilton's stationary action is: the true trajectory is the point in variation space such that the derivative of Hamilton's action is zero. Whether the condition of derivative-of-Hamilton's-action-is-zero corresponds to a minimum or a...
This question is specifically about deriving the Beltrami identity.
Just to give this question context I provide an example of a problem that is solved with Calculus of Variations: find the shape of a soap film that stretches between two coaxial rings.
For the surface area the expression to be...
In the hypothetical case of a rotating celestial body, with perfectly spherical shape: A plumb line would not point straight to the geometric center of that celestial body, due to the fact that the plumb line is co-rotating with the celestial body.
There is a connection with the oblateness of...
Well, I have argued that the two are not comparable.
Motion of the bob of a Foucault pendulum (during swing from one cusp to the next cusp) is not comparable to ballistic motion.
I suppose that people who think they are in some sense comparable are thinking in terms of the ground track of the...
The above diagram is for the case of a plumb line. The arrows in the diagram represent the forces acting on the plumb.
To bring out the angle: the oblateness of the Earth is much exaggerated.
Blue arrow: gravity
Red arrow: tension of the plumb line
Green arrow: the resultant of red and...
A recurring question is: while the motion of a polar Foucault pendulum is fairly straightforward, the case of a non-polar Foucault pendulum is quite difficult to visualize.
In 2020, on physics stackexchange someone submitted that question and I contributed an answer.
In a comment to another...
I'm writing a second reply to the same remark.
When I see some online available resource (a textbook, lecture notes) I check out whether the author introduces the work-energy theorem, and if so, how.
Many authors do not introduce the work-energy theorem at all, and the ones that do often give...
I am very eager to address this.
Among the standard tools of classroom demonstration is an air track.
(And nowadays, if the school does not have the money to buy an air track, the students making their first steps into Mechanics can watch air track demonstrations via internet connection.)
I...
Then by all means the work-energy theorem should be taught in a way that minimizes the likelyhood of confusing new students.Many sources use Torricelli's equation to supply the relation between acceleration, displacement, and change of velocity:
##v_i## initial velocity
##v_f ## final velocity...
Among the purposes of the post is to probe what in general the attitude is (among the readers of the 'classical physics' forum) towards the work-energy theorem.
I am of the opinion that there are no new results in the narrative that I present.
Different authors derive the work-energy theorem in...
I have replaced the image with MathJax/LaTeX.
To make up for the unnumbered line in the image version I stated those relations as (1.1) and (1.2)
(I tried to replicate the layout of the image version with LaTeX syntax, so far no luck.)
The work-energy theorem is the connection between expressing mechanics taking place in terms of force-and-acceleration, ##F=ma## and representing mechanics taking place in terms of interconversion of kinetic energy and potential energy.
The following statements are for the case that there is a...
It appears there is an error in the database that powers Ian Bruce's website, resulting in a shift.
This is the link to:
Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu acceptiThe URL of the main page, which lists...