The h Bar

7:44 AM

How does the configuration space work exactly in Lagrangian mechanics

Is it "The space of functions with values at $t_a, t_b$ set to the boundaries"

I'm not sure of the exact formal way to put "the variation from the Gâteau derivative is zero at the boundary"

Because that function space doesn't form a vector space

Unless the boundary is zero

Since if $x(0) = 1$, then the sum of two such functions $x_1(t) + x_2(t)$ will be $2$ at the boundary

2 hours later…

Loong

9:21 AM

> So, per pound, coal has more energy per kg.

ouch

9:49 AM

:-/

10:03 AM

@Loong you maybe interested in this

10:14 AM

that's why my smartphone runs on coal

as opposed to ?/kg :P

Loong

@skullpetrol omg :-(

yikr

~~interested in~~ depressed by

10:46 AM

in Mathematics Educators, Aug 3 at 15:14, by skillpatrol

silly-troll-question

Loong

11:13 AM

@skullpetrol I put my usual reply as an answer since it's too long for a comment.

thanks pal :-)

Duty calls

cya

11:52 AM

Bitbucket is sunsetting Mercurial support

¬¬

damn

@DanielSank and his tribe have won

did you hear, the boxing legend César Chávez got mugged at gunpoint in Mexico City?

@skullpetrol Cesar Chávez?

(The boxer is Julio César Chavez, and no, it's not the same name if you randomly drop bits from it)

In any case

"person gets mugged at gunpoint in Mexico City" stopped being newsworthy many decades ago, I'm afraid

independent.co.uk/sport/general/boxing/…

> Mexico is currently suffering from record murder levels that have made the capital, long regarded as a relatively safe haven, increasingly prone to outbreaks of violent crime.

> long regarded as a relatively safe haven

lol

sorry

that's some amazingly short-termed memory

Mexico City was long regarded as one of the least safe cities in the country

definitely through the nineties and into the early 2000s

it's only in the late 2000s and early 2010s that the crime level elsewhere rose enough to overtake the capital

crime in Mexico City never really went down

12:09 PM

hmmm

but in any case, "oldish guy gets mugged" is pretty far down the agenda these days

lol

oldish boxing legend :-)

cases of police officers raping women are a bit more of a pressing concern

>8(

↑ exactly

so, sorry if I can't work up an indignation about a watch getting stolen

¯\ _(ツ)_/¯

12:15 PM

Cartel-Ravaged Mexico Sets a New Record for Murders

also Murders in Mexico rise by a third in 2018 to new record

@skullpetrol 2018 data is aging extremely fast

the crime level everywhere rose to overtake the capital :O

the new government started on 1 December 2018

so we don't have a full year of data yet

and it will take some time to process

but the environment is different now

(not necessarily for the better, though)

so any data prior to 2019 needs to be understood within that frame

@skullpetrol ::facepalm::

what?

there's more governments than the US government, you know

oops, i keep thinking about the silly "wall" :-)

sorry

sorry, but

12:27 PM

lol

I thought this was a serious conversation

that's my cue, though

see you around.

cya

2 hours later…

2:10 PM

@Slereah why does the value taken at the boundary matter, e.g. in extremizing the arc length $S = \int_a^b \sqrt{1+y'^2}dx$ it doesn't matter what values $y$ takes at $a$ and $b$

2:26 PM

@bolbteppa well there is a boundary term to the EL equation

The $h$ in $S[\phi + \varepsilon h]$ would not cancel out if we didn't have that all functions on that function space vanish at the boundary

I do recall that the Wiener process (heheheh) is defined on functions with compact support on $[a,b]$, which may be related

Oh right, hmm

I do suppose you could decompose any function with boundary condition $x(0) = x_1$ and $x(T) = x_2$ by some random function with those boundary conditions + the vector space of functions with compact support on [0,T]

mb that is the trick

That's a good point

About the functional being defined on a set of functions with specific values at the endpoints, is it a vector space

Well, as I said

it is if the boundary is zero

It seems like a fairly basic issue but I can't find anything specifically on the topic

it might be because I look it up with physicist words

and they don't care too much

I'm looking in Gelfand's COV

It begins by setting up linear functionals on normed function spaces and defining a norm useful for COV but then when discussing EL eq's it just talks about the 'set of functions with boundary conditions $y(a) = A, y(b) = B$' i.e. the subset within that normed vector space satisfying the BC's, I don't think they have to be a subspace

The EOM don't have to be linear so no reason why they should form a subspace in general right