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00:01
Another courser?
@Slereah
Wonder if ACM has the game yet
vzn
vzn
(spking of "nuking"...) wow, thought had seen it all... a physics urban legend...!
00:26
Welp
Courser wasn't so tough
00:43
@Slereah about to enter the Institute. What should I expect?
Dunno
Building the teleporter myself
@Slereah who are you building it with?
I fucked over the Railroad and chose Brohood
I came across the equation$$\partial f(x)=\text{co}\left\{ \lim_{i\to+\infty}\mathrm{d}f(x_i)|x_i\mapsto x,x_i\notin S\cup\Omega_f \right\}$$Does anyone have an idea what the $\text{co}$ means?
GIMME THE MONEY
I HAVE ALL THE SPOILERS
Railroad
Should have picked the Brotherhood
I have to build it out of tincans
00:57
Lel
The brotherhood gives you the parts
BTW this plot makes less sense than Bioshock
spoilers lol
uh
I just killed the son
@Slereah help
get a new wife, make a new son
I think the Brohood wants me to kill everyone here
Are you in yet?
I don't know what to do
Dunno who I want to betray
I have no clue what's happening
@Slereah where are you?
yay I can now fast travel to the Institute
Bethesda, why are your games so good...
01:20
I'm in the institute
They'd better not fuck it up because I have a power armor, a nuclear launcher and 30 nukes
Woah what level are you
They're not gonna do anything.
In interested to see what happens
Do you always run around in power armor?
No
I put it on for the institute
About level 50
01:36
@Slereah you killing everyone inside?
Nah
Exploring a bit right now
If I don't like what I see though
There's gonna be heck to pay!
01:51
@Slereah let me know what you end up doing
did the Railroad give you some kind of mission to do while in the Institute?
I got two from the brohood
dunno if I should do them!
this is nuts
obe
obe
what game are you talking about?
@obe do you live under a rock
obe
obe
idk, do i?
02:07
maybe...
02:17
@dmckee I'm more dismayed that there are people who actually vote those "free energy" posts up.
@ACuriousMind It's possible that someone is running some socks. Time will tell, but I won't.
@dmckee It's good to help people understand how these free energy demos fail.
It can be really hard for a beginner/untrained person to understand.
@DanielSank Oh, no argument from me.
@dmckee In fact, I asked this one
84
A: Where is the flaw in this machine that decreases the entropy of a closed system?

DanielSank Thus, the air molecules contribute a small portion of their kinetic energy to the paddle, which is then expended as heat on the other side of the border, making the air molecules on the left colder, while air molecules on the right heat up. Doesn't this mean a decrease in entropy? Yes it doe...

to a bunch of physicists and nobody got it.
But I don't understand the way the younger generation looks to video for information and just watch every thing that comes by.
02:24
@dmckee Oh well yeah. I find videos really inefficient for learning anything that isn't hands-on, e.g. fixing a car.
Yeah. Low density, imprecise and hard to search.
Videos for demonstrating programming etc. are completely ridiculous.
"Here's a tutorial video on how to install our software."
::closes window immediately and doesn't use software::
3
02:50
@DanielSank good to know I'm not the only one
03:06
I could use some numerical analysis help if anybody is willing to take a stab at something... I'd ask on SciComp but unless it is about Petsc it won't get answered.
user54412
@tpg2114 me me me! pick me!
@ChrisWhite Brilliant! I need to do some von Neumann (Fourier) stability analysis for a scheme and I'm having an impossible time figuring it out
user54412
no guarantees though ;)
I need to generate contour plots of the amplification factor, let me find you an example...
user54412
while you're doing that, @tpg2114 did you ever see this message?
user54412
03:09
Nov 3 at 5:34, by Chris White
For anyone other than @tpg2114 and me who's interested in colormaps: matplotlib is now including perceptually uniform sequential colormaps, and in fact one of them will become the default!
user54412
I'm curious to hear your opinion on the new suggestions
@ChrisWhite Nope, I missed that one... Weird. I guess I hadn't been in chat recently enough?
Do you still have journal access to things?
user54412
yep
Or do I need to find a non-paywalled source
I need to generate plots like Figure 1 and 2
For a dual-time scheme like Eq (2) in same
2D Euler equations, nonconservative form is okay (so \Gamma \partial Q /\partial \tau + T \partial Q / \partial t + A \partial Q /\partial x + B \partial Q /\partial y = 0) where \Gamma is a matrix, T is a matrix, and A and B are the flux jacobians
Where I am horribly confused is that I have 2 "time steps" -- a physical time t and a pseudo-time \tau, and so I end up with 2 amplification factors
And no idea how to deal with that.
user54412
I'm trying to wrap my head around this
user54412
03:13
\tau somehow accounts for substeps?
Yeah... okay, so a dual time framework adds a new, pseudo-time derivative to the Euler equations
And the physical time term becomes a source term as you iterate in pseudo time
As pseudo time -> infinity, \partial Q /\partial \tau -> 0
And you are left with the original equation
Jameson came up with it originally in like... 1981 or something. I'm using it to turn an explicit scheme into an implicit scheme. The physical time derivative is discretized with an implicit formulation, like a backward Euler, and you can choose a physical time step to be as large as you want (since it is implicit). And then you march in pseudo-time with an explicit scheme like RK4 and when your pseudo time derivative becomes close to zero, you are at your chosen physical time
Eq (7) is the discrete scheme you end up with -- the LHS is the update to the pseudo-time level and the RHS is the physical time derivative (using a 2nd order backward difference here) which acts as a source term, and the spatial fluxes R
user54412
As this is my first exposure to this particular scheme, I can't decide if it's madness or genius
Heh, I think it's brilliant
If you have an explicit code -- well validated, efficient, correct -- you can turn it into an arbitrary order implicit scheme by adding a source term
And then if it's low Mach number, you can use preconditioning as well to eliminate the stiffness, but you don't need to do that if it isn't stiff
user54412
::wonders if this would be so trivial in GR::
Although I may be biased in my view of it since it is the bulk of my thesis
user54412
03:22
"Extension of the method to 3-D is straightforward."
It actually is, don't worry :)
This paper: arc.aiaa.org/doi/abs/10.2514/3.12946 has everything you would need to do it
It has the 3D form written out
user54412
okay, so a lot of this paper is about preconditioning, but I'm thinking I can ignore that?
Yup
Just say \Gamma is a matrix and you don't really care what it looks like
Basically I need to figure out the amplification factor for Eq (7)
Assuming \partial A /\partial x = 0 and \partial B /\partial y = 0 because we're pretending the equations are linearized
And for fun, R can be central differences in X and Y (explicit, so based on the values of Q^k)
user54412
so there's some warning about the approximations needed for viscous terms to work
user54412
but you're not asking about that, right?
user54412
03:26
just assume everything is well diagonalized and hyperbolic and happy
Correct, Euler only
The problem I have is that I get an amplification factor for pseudo time from Q^{k+1} = G^k Q^k
And a second one from Q^{n} = G^n Q^{n-1}
which is the physical time amplification
user54412
so what to do with them?
And so I have no idea how to plot contours of |G^k| without knowing anything about G^n
Unless I just assume values for G^n, like -1 <= G^n <= 1 (because I am assuming my physical time scheme is stable)
But then they only show one set of contours as a function of Mach, CFL, and x- and y-wavenumbers
Not as a function of G^n
So maybe there's some assumption about it or relation or something that could be made that I'm missing
user54412
btw you keep using G
user54412
in the paper, G is just the z-fluxes?
03:35
G being the amplification factor matrix (not in the paper)
Sorry for the confusing notation
G is the amplification matrix arising from the von Neumann stability analysis -- Q^{k+1} = G^k Q^k
And the scheme is stable in pseudo time if | G^k | <= 1
Here, this one is easier to follow cause it uses the same notation I do:
Section D
The lead author on this paper is funding my thesis and when I asked him how to do it, he laughed and said "It's really easy, go look at (the paper I just sent you) and you can figure it out from there"
And... I can't figure it out
user54412
I've had people say something is "easy" and then they send me the actual code that does it and I still can't make heads or tails of what they're doing
Yeah, I'm afraid to ask again cause he's a really big name, and working to get funding for me for next year, and on my thesis committee...
But I've asked all 4 post docs in our lab and all the students in the lab and none of them even remember how to do von Neumann analysis so it was kind of a non-starter
(Side note -- arc.aiaa.org/doi/abs/10.2514/6.2001-2591 uses a dual-time scheme for the MHD equations; I bet you could do it for GR and with a proper preconditioning matrix, make everything hyperbolic and well conditioned)
user54412
GR is actually always hyperbolic and, as far as I've encountered, always well conditioned. And people think GR is hard ;)
Really? No low Mach number flows in GR?
I guess not... speed of sound is probably nowhere near speed of light in anything ever
MHD is not well conditioned, just because light is so much faster than sound
user54412
I think the important thing is that all speeds are bounded by c
user54412
03:46
I think of it as not that nothing is slow, but rather that nothing is too fast
But what are the eigenvalues of the characteristic system? You don't end up with the traditional Euler {u, u, u, u+c, u-c} (c being speed of sound there)?
user54412
Yeah -- so it's basically the same as the Euler system (plus some funny terms for the sound waves). So if you have a low "Mach" number (whatever that means exactly) then it will be ill-conditioned
user54412
user54412
If anyone has written the equations in full GR, I don't want to see them
user54412
03:54
@tpg2114 yeah, but in practice this rarely happens
user54412
or maybe it's just ignored :p
That's what I figured... Although if you are doing radiation or MHD, it will show up because the speed of the Alfven waves is much bigger than the speed of sound or the particle velocity
user54412
well, I guess often our fluids are often radiation-dominated -- the "sound" waves have radiation pressure as a significant part of their restoring force
user54412
in the limit p_rad/p_gas -> \infty, iirc the hydro sound speed goes to c/\sqrt{3} or something
Yeah... I'm totally happy to be running problems at 5 m/s composed entirely of air
user54412
04:00
what's really awful is when the plasma is so hot you get pair production -- no more rest mass conservation
I'm running a jet in crossflow right now to compare the preconditioned scheme with the explicit scheme -- the solutions are night and day different
I'm actually pretty shocked at how different they are
Oh... more random questions for you @ChrisWhite... have you done any cosmological simulations? Or know anybody who has? I'm interested in doing some topological analysis using something like Reeb Graphs or Morse-Smale complexes, but I can't really figure it out
I found this library: www2.iap.fr/users/sousbie/web/html/indexd41d.html? and I'll play with it at some point, but I like to have a better understanding of some nuances to the algorithms before I just use them blindly. I've written a little code that can compute the complexes for really simple functions but then it doesn't work on real problems
user54412
I know of a lot of people doing cosmological simulations, but I thankfully haven't
user54412
actually they're quite straightforward except for the fact that they're essentially Newtonian with self-gravity
user54412
and of course Newtonian gravity is Poisson's equation, so it's all about elliptic solves and all-to-all MPI communication
Yeah, that's why I want to use preconditioning instead of incompressible... those damn global communications are brutal
user54412
04:11
(there's also lots of "subgrid modeling" that needs to be done better, like accounting for how a newly-formed galaxy will have a burst of star formation and supernovae that put out energy and momentum, but all of this on much smaller scales than a single cell, but this doesn't affect the post-processing topology stuff)
user54412
@tpg2114 the vast, vast majority of the matter in the universe is a highly compressible plasma :p
I also dislike subgrid modeling, but since I work in large-eddy simulation, I didn't just say that
user54412
There's an emeritus at my department (and has been emeritus for a long time if you catch my drift) -- Rich Gott -- who's done a lot with cosmology topology
user54412
that said, I don't think there's any sort of final word on it
I just want a non-peer-reviewed, non-jargon explanation of how to do it... hah
user54412
04:17
btw I'm no less confused than you about these amplification factors
user54412
all these plots show the explicit scheme and the explicit+pseudo time scheme, right?
user54412
or did I miss something already
user54412
actually, I need terminology help -- what does your field mean when you say CFL = 10?
CFL = \lambda dt /dx
user54412
ok, so CFL=1 is marginal stability for explicit hyperbolic equations
04:21
And no, you didn't miss anything -- the plots are the non-dual-time scheme and the dual-time scheme. I think both of those papers use an implicit scheme for pseudo time and an implicit scheme for physical time as well
Correct. So in my code, my pseudo-time is explicit and physical time is implicit. So I run my pseudo-time at CFL_pseudo = 0.5 and CFL_physical = whatever I want (usually 100-1000)
If my pseudo time were implicit (like these papers), I could run at whatever is stable for it (so CFL_pseudo = 1000 or whatever)
user54412
ok, so CFL_\tau is just set to be 3 usually in the paper
user54412
and the timesteps are chosen either to make the particle/contact/entropy wave have a certain CFL number (CFL_u) or to do the same for the sound wave (CFL_{u+c})
user54412
so if CFL_{u+c}=1, CFL_u will be really small and you'll wast cycles in some sense
user54412
and if CFL_u=1, CFL_{u+c} will be large and you'll have large amplification?
Basically, yes
Although with preconditioning you get good amplification at CFL_u = 1 (that's the benefit)
user54412
04:30
right
user54412
so Eqn 6 in that last paper is the amplification for the whole scheme?
user54412
it's certainly aware of both timesteps
It's for a 1D scheme, but basically
What drives me crazy about that is he doesn't explain how he gets it -- if you take Eq (3)
And make it 1D
You get \Gamma_p \partial Q_p/\partial \tau + \Gamma_e \partial Q_p /\partial t + A \partial Q_p /\partial x
Where \Gamma_e = \partial Q/\partial Q_p converts conservative to primitive
And then, if you discretize the pseudo time derivative with a backward euler, the physical time with another backward euler, and the spatial with a central scheme, you get:
\Gamma_p (Q^{k+1} - Q^k) + \Gamma_e \Delta \tau / \Delta t (Q^{n+1} - Q^n) + A \Delta \tau/(2\Delta x) {Q^{k+1}_{i+1} - Q^{k+1}_{i-1}) = 0
And you assume that you are marching to Q^{n+1} and Q^{k+1} is an approximation to it, so you replace Q^{n+1} by Q^{k+1}
To give you:
\Gamma_p (Q^{k+1} - Q^k) + \Gamma_e \Delta \tau / \Delta t (Q^{k+1} - Q^n) + A \Delta \tau/(2\Delta x) {Q^{k+1}_{i+1} - Q^{k+1}_{i-1}) = 0
And then you do the von Neumann analysis on that and hopefully end up with Eq 6
Which I can do, but only if I make a weird assumption to deal with Q^n that I don't understand...
So my total VN analysis is:

\Gamma_p (G Q^k - Q^k) + \Gamma_e \Delta \tau / \Delta t (G Q^k - Q^n) + A \Delta \tau/(2\Delta x) {G Q^k exp{i w\Delta x} - G Q^k exp{-iw \Delta x}) = 0
And if these were scalars, you would divide by Q^k, since they are vectors/matricies I guess you right-multiply by inv(Q^k)
But either way, I get:

[\Gamma_p + \Gamma_e \Delta \tau / \Delta t + A \Delta \tau/\Delta x i sin(w \Delta x)] G - \Gamma_p - \Gamma_e \Delta \tau/\Delta t Q^n inv(Q^k)= 0
Which gives Eq 6 if somehow \Gamma_e \Delta \tau/\Delta t Q^n inv(Q^k) = 0, but no idea how the heck that happens
I know to start things up, at the very first pseudo iteration, Q^k = Q^n, but then that term would be = \Gamma_e \Delta \tau / \Delta t and not 0 so I don't know how that works
user54412
04:45
2 hours ago, by tpg2114
As pseudo time -> infinity, \partial Q /\partial \tau -> 0
Yeah, but G is the amplification factor in pseudo time
So I don't know how that related to Q^n
user54412
I was going to say this might help but on second thought I don't know
So my actual problem has both a Q^n and Q^{n-1}
And since I can't even figure this one out, I'm super lost on my real problem
user54412
So \Gamma_e is some order-unity thing
\Gamma_e converts conservative to primitive variables
user54412
04:48
yeah
It doesn't really have an order to it
user54412
Can I not just say \Delta\tau << \Delta t
You could, but then why retain it in G?
If you do that, it would go away everywhere
Not just in that Q^n term
user54412
good point
And it's not required that \Delta \tau << \Delta t
Although it often is in practice (in fact, you can march to the time invariant problems by taking \Delta t >> 1. I'm running simulations to steady state with \Delta t = 1e20 right now)
But for time accurate simulations, those terms stick around
user54412
04:53
have you tried petsc? :p
Haha, good one
I'm supposed to have a meeting with the sponsor on Tuesday. I may just have to walk through the derivation to this point and ask WTF he did to that term
It's a bummer nobody else seems to know how to do it either, but it's a little bit reassuring that I'm not like... stupid or something
4 post docs and a number of PhD students couldn't answer it
How's your real work coming?
user54412
I feel there's something fundamental I'm not understanding with the two times floating around -- something about simultaneously discretizing them seems... off?
If I have something like this i.gyazo.com/d832feb08f8dc5262d96d6fff3237f32.png, is the only torque about G due to T? It's not slipping.
user54412
Anyway, my work is going okay. I finally got the method paper out for our code, so now I can focus on doing science.
05:08
Part of me feel like friction has to come in...
user54412
And my thesis committee has made it clear that I had better start doing science, now yesterday.
But I have no clue how to get friction
user54412
rolling w/o slipping -> static friction
@ChrisWhite This analysis is holding up my methodology paper...
@ChrisWhite exactly
so I have way too many unknowns...
user54412
05:09
static friction is whatever it has to be -- you solve for it
I don't know the acceleration
user54412
@tpg2114 your field is clearly more numerically advanced than mine
user54412
there's a delay of 20-30 years between when methods are invented and when they are brought into GR MHD
You mean "Everybody else but you in your field..." since I can't figure this out :)
@ChrisWhite Do I consider $T$ and $f$ for Neton's law on the CM?
that might work
05:12
Well, this dual time thing is 30 years old, preconditioning is 25 years old and I'm the first one to apply a scheme from the 60's in the dual-time framework, so I can't say I'm super modern
user54412
@0celo7 maybe -- I hate these sorts of problems
this might work
I get $T-f=ma$ and $rT-Rf=I\alpha$
o.o how are $a$ and $\alpha$ related when there are two radii
probably use the biggger one
yolo
haha it's rolling backwards
ha
crap
@0celo7 Assume a sign is wrong and flip it at the end ;)
ha!
the denominator is negative too
but wow 23 rads per sec^2 seems like a lot...
user54412
numbers...
05:20
I know right? Symbols or floating point values on a grid.
Anything else, not worth it
@ChrisWhite You use Visit for your visualization, right? Or am I mis-remembering...
ok
assuming all of that is correct
now I have to find the min coeff of static friction
that's when $f=\mu N$, right?
user54412
@tpg2114 yes, especially for on-the-fly stuff, 3D, and complex grids
user54412
I never quite liked the final output, though, so pretty pictures I try to do in matplotlib
Do you have licenses for FieldView? Apparently they partnered with Visit now and can do in-situ visualization
We abandoned FV years ago, I use Paraview now and I have it hooked up to our code for in-situ analysis
....
user54412
05:22
FieldView? have not used it
negative coefficient of friction
that's awkward
user54412
yay perpetual motion!
ah, it would help if I used linear acceleration in Newton's law
yay .24
that's not crazy
I think I'm correct
@ChrisWhite Big presentation file: mcs.anl.gov/~hereld/doecgf2014/slides/… and a lecture on using it in-situ: nas.nasa.gov/publications/ams/2015/01-16-15.html
user54412
you know, I'm chatting on my windows machine, but I'm turning around to my mac in order to load ppt
05:25
Really?
good man.
I have a 181MB PPT about Paraview and in-situ processing
user54412
wow this presentation reminds me how much industry cares about CFD
Holy crap that's big
user54412
(it doesn't care about astro, or fusion plasmas, and that's all I see these days)
05:28
Yeah -- FieldView is having a webinar next week I think about visualization for the Formula1 teams they work with
Good visualization is important everywhere though, not just industry
It just isn't given proper consideration in my field
It's all 2D slices colored in rainbow
user54412
^ all too true
People should lose their funding if they write a report or paper that uses rainbow or spectrum
It should be as bad as falsifying data.
Do you guys do anything with tensor invariants? Like for turbulence there are P, Q and R which are the 3 invariants of the velocity gradient tensor
P is the dilation, Q is the relationship between strain rate and rotation rate, and R... nobody has a good explanation of what R is really
user54412
some people might
I was trying to think of what the invariants of the vorticity gradient tensor would be... but I can't wrap my head around it
And nobody has published anything about it
user54412
but mostly I see vorticity, helicity, curl, divergence -- all much nicer to visualize :)
05:34
We use Q to visualize coherent structures in a flow
user54412
lemme guess: butterfly?
The top is Q -- 1/2 (|\Omega|^2 - |S|^2)
The lower left is vorticity, lower right is species mass fraction of the jet
Butterfly?
user54412
looked like a Rorschach test :p
Ah, haha... Jet into a crossflow
From the side (top), from behind the jet (lower left) and isometric of the front of the jet
The top and bottom left are two different ways to visualize strong vortices. It's really cool, it creates those upright tornado vortices
They drop from the jet and make contact with the bottom wall
user54412
Oh random thing I remembered to tell you: If you want cosmological simulation output, some big names are Millenium (though I don't know how much of the data is public) and Illustris (which has all the data available for download).
05:44
Sweet, more data to play with
user54412
the latter one uses an... interesting grid
user54412
moving mesh, with voronoi tesselation redone every timestep or something
We have some demographic data based on zip code for a non-profit I am part of and so I was learning fun data analysis stuff in Python. I have a script that downloads all the zip codes in a state, all the highways in the country, and then plots them on a map and I'm working on contour/heatmaps for the zip codes and stuff
I could get it to download counties, congressional districts, area codes... all kinds of stuff
user54412
data visualization can be kind of fun
Python and matplotlib is magic
Yeah, I really like data visualization and trying to come up with good ways to analyze high-dimensional datasets
The in-situ stuff I'm doing with Paraview is to try and identify structures of interest during the simulation and them trigger file and image output when things start to appear or disappear
user54412
05:48
That's something I've never played around with, but I can see it becoming more necessary.
That's why I've been digging into the invariants
user54412
You don't want to be post-processing yottabytes of data
Exactly -- that 3 view of the jet was done during the simulation. It was outputting those frames every 1000 time steps
It can also be setup so I can connect to the simulation while it's running and look at the solution interactively, that's pretty cool too
user54412
ooo fancy
It's actually really easy to set it up in a code if you are interested :) I'd be happy to help if you go that route
If you know how to use VTK, it's not bad. If your code uses VTK data structures already, it's super simple
user54412
05:51
I don't suppose it's on Mira? We just got a chunk of time on that.
user54412
VTK was our default output for many years (though now we favor HDF5)
Doesn't look like it's installed on Mira, but you can build paraview from source (although it can be annoying sometimes)
It is on Tukey though
Ohh, and the paraview mailing list claims it is on Mira: public.kitware.com/pipermail/paraview/2014-February/030600.html
There is a presentation that says:

> /soft/visualization/paraview/v4.1.0/catalyst/<edition>
Where <edition> is:
base[+essentials][+extras][+python]
Catalyst is the co-processing library
on Mira
I don't have access to that machine so I can't poke around
user54412
I won't have access for a couple weeks, but I'll keep it in mind
If you do want to try the in-situ thing, let me know and I can walk you through the steps of getting your code ready.
Is it in C/C++ or Fortran?
user54412
C++
05:59
Psh, that will be simple then
user54412
^ words not often said of C++
Ours is Fortran and never used VTK... so I had to take the C++ VTK stuff, extern it to C, wrap the extern C routines into C routines that Fortran could call, then write the Fortran module to call them from our code
And then I had to dig into the guts of VTK to figure out how to not duplicate the data in the VTK data structures from our arrays and to instead store a pointer to our memory. So I have to get a pointer to Fortran memory to go from Fortran -> C -> C-wrapped C++ -> C++
And the pipeline used during the simulation is a python script, so it's really a big jumble of languages working together
user54412
Hmm, I have a meeting in too few hours. I should head off.
user54412
Good seeing you again @tpg2114 And I'll think more about this pseudo-time thing.
@ChrisWhite Thanks for you help, if you have an epiphany, ping me :)
 
1 hour later…
07:10
1
Q: An incomprehensible warning

frankI was about to ask a question, when this warning appeared: Wait! Some of your past questions have not been well-received, and you're in danger of being blocked from asking any more. For help formulating a clear, useful question, see: How do I ask a good question? Also, edit your...

 
3 hours later…
09:42
What is the physical "meaning" of the Lagrangian? I would think $T + V$ instead of $T - V$ would be more "geometrically meaningful" in the sense that $T + V$ of a particle moving through a specific trajectory represents the total energy of the particle on that path. The intuition I have for $T - V$ is that it's the total energy the particle "uses" during moving through that path. Is that the correct interpretation? If not, what is the correct "meaning"?
That said, the action $S = \int L dt$ should represent the total energy use during traversing the path, right?
I am not sure that the Lagrangian has a strict physical meaning. Physically, it is rather "intuitive" (but that could be disputable) to use position and velocities as the data of motion, since the equations of motion are of second order in time. And the lagrangian is the "generator" of dynamics (via E-L equations) with position and velocities as variables.
I mean, the whole point of Lagrangian formalism is to minimize $S$, right? Why try to do that in the first place if we don't know what $S$ means? I am completely befuddled.
minimize $S$ ;-)
Whoops, typo.
historically, for sure it went the other way around
first there were Newton equations
09:52
In my interpretation, it means particles traverse in path in which the total energy use is minimized. That I can believe.
I may say that work is much more closely related to the concept of "energy used"
at least for my personal intuition
Yeah, that's precisely what I think it means.
but the work and the lagrangian are not the same thing :-P
oh, I misread.
what do you mean by work?
In physics, a force is said to do work if, when acting on a body, there is a displacement of the point of application in the direction of the force. For example, when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). The term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis as "weight lifted through a height", which is based on the use of early steam engines to lift buckets of water out of flooded ore mines. The SI unit of...
of course only the displacement in the direction of the force counts (so for example the magnetic field does no work)

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