The h Bar

12:01 AM

You refused to spend 30 seconds reading my proof and you expect me to read this

moonwards.com/machines2.html#TetherTransport

i seriously doubt anyone can evaluate any proof in 30 seconds. and you don't have to read it, but if you are interested in understanding this, it is the fastest way to do so.

Phase

It was a rudimentary proof of a basic fact

it was more of a derivation

kim holder

the second link has a really simple animation just under it, that gets across the mechanism quickly

Phase

Just to show you that there's only one force, and nothing resists that force

Whoaaaaaaaaaaaaaaaaaaaa

that animation is either massively wrong or needs some serious labels

What force is it subject to that causes it to move up the tether

There is no centrifugal force her

*here

kim holder

that whole section is due for overhaul. but it climbs the tether. until it gets beyond the center of gravity

Phase

12:05 AM

Why does it climb the tether though

What force is it subject to

kim holder

why do cars go down the road?

Phase

Because they're moving at a constant velocity

kim holder

it's a very simple animation, it can't explain everything.

Phase

What force is being exerted to do work against gravity?

kim holder

what i was implying is the climber is powered.

Phase

12:06 AM

Ok

Why does it continue moving outwards after the tether ends

kim holder

but once it was a ways beyond the center of gravity, it wouldn't need to be powered

Phase

The rocket uses thrusters?

No

kim holder

pick whatever name you want for that force, but there is an outward force on the tether at that point

here, let me get the snippet from the javascript. the math isn't mine, but i can assure you it is solid.

Phase

There is no force on the Rocket other than Gravity that is not generated by the structure

*or the rocket

@0celo7 @DavidZ @BalarkaSen someone pls help explain

kim holder

look, if you want to see what i mean, you are really going to have to think about it for a while, and the best way to do that is to read the links, especially the one to Hop's Blog. I am not good with the math or the physics, but i assure you, there is an outward force there, and people who are excellent with these things explain it at those links

0celo7

12:09 AM

what now

Phase

The outward force must be generated by the structure or the rocket

Centrifugal force does not exist in the animation you sent

Because the frame of reference is nonrotating

kim holder

the tether is rotating around the planet

Phase

Yes but the co-ordinate system isnt

kim holder

and you don't like me saying centripetal

Phase

Well no, but that doesn't mean centrifugal works either

Again: the rocket is only subject to a force from itself or the structure

You can't just have something accelerate for no reason

kim holder

12:12 AM

thus the use of centrifugal

Phase

...centrifugal DOESNT EXIST

The frame of reference is NOT rotating

Centrifugal forces only exist when you consider a frame of reference that isn't inertial

kim holder

once you are beyond the center of gravity, there is an ever increasing outward force, because the tip of the structure is moving faster than orbital velocity at that altitude.

if you were on it, you would be pushed upward along the tether, and if you let go of the tip, you'd go flying off into space. Because you are in a rotating frame of reference.

DanielSank

Hi, everybody.

You spin me right round, baby, right round, in a manner depriving me of an inertial reference frame. Baby.

Phase

Daniel if you read what I said I was saying that centrifugal doesn't exist here because the co-ordinate system isn't rotating

DanielSank

Yeah, I know.

Phase

12:19 AM

o, sorry in the middle of arguments my sense of humour vanishes

kim holder

brb

(hi @SirCumference)

Phase

hang on a sec

yeah

Orbital velocity at 9500km above earth is 5000 m/s

Your calculator says that a tether with an endpoint at 9500 km above earth is like 2000 m/s

*1500 m/s

that means that a mass dropped from the top will fall back down to earth

hm I think the graph was set to the wrong settings

I adjusted it the scales and got one greater than the orbital velocity.

David Z

@Phase you'll have to catch me up on the context

Phase

@DavidZ click "replay" on the animation moonwards.com/machines2.html#TetherTransport

top left hand corner of the animation window

However

That animation really could use some labels

its gonna take some time for me to understand this spacetether lark, but what I am certain of is that it's not subject to a force. It's just that the force exerted on something with too great an orbital velocity isn't enough to constrain it to a circle.

That's not to say anythings 'resisting' it, just that F = d/dt p and the rate of change of momentum just isn't enough to move circularly

In the frame of reference given in the animation that is.

Every animation I find online has the spacetether rotating

about a point on the spacetether

0celo7

12:37 AM

@BernardoMeurer I need you

Phase

@DavidZ do you understand it?

Ok I think I get it.

David Z

Well, what's the question?

0celo7

@BernardoMeurer urgently!

Phase

I was confused as to why it acted like a rigid object rotating around earth without any rotation about a point on it, when its velocity at the tip is greater than the orbital velocity at that point, but it doesn't, it rotates about a point on it

DavidZ not entirely sure but I just meant do you understand the animation

@kimholder I think you need to fix your animation

So the tether rotates

Bernardo Meurer

@0celo7 I'm here

Phase

12:42 AM

Otherwise if I dont have my wires crossed, every point on the structure must have a velocity equal to the orbital velocity at that point

Bernardo Meurer

@BalarkaSen I have some nice ideas on my write-up, hit me up when you're around

0celo7

@BernardoMeurer I need to do a German placement exam

We need to practice our German

Phase

As if it had a greater one, it would exert a torque and start rotating it anyway

David Z

@Phase Oh, OK. I think so. At least I understand the sequence of events it's showing.

Phase

Do you agree with me David

Kim claims that the end is moving faster than the orbital velocity at that point

0celo7

12:43 AM

ayy thermal science homework isn't due until monday

ok @Phase what is it you need?

Phase

moonwards.com/machines2.html#TetherTransport

click replay on the animation

Apparently the end of the tether moves faster than the orbital velocity at that point

Bernardo Meurer

@0celo7 My German is horrible, it's been literally years since I even used it at all

0celo7

@BernardoMeurer same

Phase

Also the tether isn't rigid

It's flexible

Bernardo Meurer

I don't remember declinations tbh

David Z

12:44 AM

@Phase I'm not sure offhand, not without doing a calculation, but that seems plausible

0celo7

my life depends on me speaking German at an intermediate level tho

@ACuriousMind can you help?

Bernardo Meurer

I can try to help

Phase

@DavidZ wouldn't it exert a torque and start to rotate the structure though?

Bernardo Meurer

I'm willing to chat in German with you for an hour a day or so

0celo7

@BernardoMeurer yass

@BernardoMeurer I'm driving to Kevin's Friday afternoon. Assuming you're not at the bottom of a pit swelling your liver, we should talk then

Bernardo Meurer

12:46 AM

@0celo7 Sadly I probably won't be

I wish

David Z

@Phase If so, I'm not seeing it... the forces are purely radial as far as I can tell

Phase

hm

Would the bottom not lag angularly w.r.t the top?

The bottom's linear velocity is lower than the orbital velocity at that point, and the top's is greater than the orbital velocity at that point

David Z

That's not what the animation shows

Phase

ik its not but their calculator does

the velocity I mean

0celo7

@BernardoMeurer ok I've got to practice for these damn talks

should I practice in german lol?

Bernardo Meurer

12:50 AM

Lol

Phase

also every other animation I find has the tether rotating about a point along it's length

Bernardo Meurer

That'll be a mess

Phase

as well as around the Earth, in a parabola

David Z

Ah, well if you just think about a cable suspended in space like that, then yeah, it might rotate

but really, I'd want to do (or see) the relevant calculations before coming down on a position

Phase

I only calculated the orbital velocities. So far all I've got is that $v_{bottom} <<$ orbital $v_{bottom}$ and that $v_{top} >> $ orbital $v_{top}$

fixed

David Z

12:56 AM

I guess I don't have time right now to properly work through this

My preliminary thought is that you have to account for the tension in the cable while computing the actual speed of different sections - but still, you might be right that it would rotate

Phase

I'm having mental block, could you give me a clue about how to actually compute it roughly

But even if there's tension, it only acts in the direction of the length of the cable

so it couldn't counter a leftward lag could it?

It would just keep the length constrained

And make the bottom and top trace out circular paths?

0celo7

@BernardoMeurer how should I practice this

David Z

@Phase Not right now. Maybe I can come back to it later.

Bernardo Meurer

Your presentation?

Phase

@DavidZ Fair

0celo7

12:58 AM

yeah

Phase

Btw

Is Stackexchange a useful resource to have? If I was to build up some rep later down the line when I can be of value to the site, would it be something to say, put on a CV or application to some position?

Bernardo Meurer

@0celo7 Rehearse by presenting it to someone

Phase

provided the rep was answering questions, I assume asking them would be less useful

0celo7

@BernardoMeurer I've already done that and it wasn't enough

I need to rehearse to people who can ask intelligent questions and those people are in short supply

Bernardo Meurer

@0celo7 Do I qualify?

David Z

1:01 AM

@Phase That I can address: it depends on the audience. Computer programmers might be impressed by a high rep on SO. Academics generally would not be.

Phase

I see. I can never decide whether to keep my account or not

I've deleted it like 3 times

Bernardo Meurer

I like my SO account

Phase

this site and I have a love-hate relationship

Bernardo Meurer

Even with all of the stupid questions in there

I think it shows that I learned things by myself

Phase

@BernardoMeurer nice touch editing your profile over time

I like it

0celo7

1:03 AM

@Phase why would you delete it

Phase

Because being here makes me sad quite often

Bernardo Meurer

@Phase Thanks! Glad you like it, I was considering taking that out

0celo7

@BernardoMeurer I can't write on a board so that's no good

Bernardo Meurer

@0celo7 Get a board

Put camera far

Phase

@BernardoMeurer keep it, it's great

0celo7

1:04 AM

@BernardoMeurer ok let me see what I can arrange for tomorrow

@BernardoMeurer ayy lmao the room with the good board is reserved all day

Bernardo Meurer

There's only one good room?

Phase

@0celo7 why dont you stream it, its nearly real time and could take nearly real time questions

invite people from math and physics SE

it would double as a grand face reveal

0celo7

stream with what, my iPhone?

Phase

Yeah

Or your laptop

We'd all get to see the truth that you're one of the reptilian elite

And we could orchestrate an En Masse witchunt to restore the morality of our new globalist world

Bernardo Meurer

@0celo7 Get a classroom with a recording camera

We had those in ULisbon

Then use that as your video device on Skype

Phase

1:09 AM

You can stream with an iphone btw tho if there are no recording camera rooms left

0celo7

@BernardoMeurer We probably have those too but that seems too complicated

Bernardo Meurer

It is, but it will look pro af

And you can "be on stage"

0celo7

@Phase Look, the formal talk is given in the math building. We have streaming available but not for that seminar

and I can't reserve anything for tomorrow, I'm looking right now

Phase

wait, I thought you were just gonna get a room by yourself and practise writing stuff on the board alone my bad

Bernardo Meurer

Ask your advisor? I do that for the CE club when we can't get a room to meet

0celo7

1:11 AM

I was, but I literally cannot reserve a room for tomorrow

everything is taken

Phase

Jesus

Anything you can go to at Midnight?

0celo7

it's midterm season

Bernardo Meurer

You should get a whiteboard at your place tbh

It's useful

0celo7

@BernardoMeurer I have too much stuff and not enough room

Bernardo Meurer

Hmmm

Phase

1:12 AM

Ok how about

Bernardo Meurer

Does your library have rooms you can reserve?

Phase

wait is physically writing important

Bernardo Meurer

Here @ the CC we have these

0celo7

They're all full!

Bernardo Meurer

Dang

Phase

1:12 AM

or is it just practising disseminating knowledge through a thing like writing on a whiteboard

Bernardo Meurer

The whole day?

0celo7

libcal.utk.edu/booking/studyrooms

Phase

awwapp.com/#

Bernardo Meurer

11 PM!

Phase

If you just wanna practise disseminating knowledge through it you could use an online sim

Bernardo Meurer

1:14 AM

One is free from 9 through 12 tomorrow

0celo7

@BernardoMeurer only J has an acceptable whiteboard

kim holder

@Phase space tethers that rotate are a separate thing. It can be convenient but this case looks at one that doesn't. See the Wikipedia page on Gravity Gradient Stabilization

Gravity-gradient stabilization

Gravity-gradient stabilization (a.k.a. "tidal stabilization") is a method of stabilizing artificial satellites or space tethers in a fixed orientation using only the orbited body's mass distribution and gravitational field. The main advantage over using active stabilization with propellants, gyroscopes or reaction wheels is the low use of power and resources. The idea is to use the Earth's gravitational field and tidal forces to keep the spacecraft aligned in the desired orientation. The gravity of the Earth decreases according to the inverse-square law, and by extending the long axis perpendicular...

Bernardo Meurer

on Thursday J has some free time

0celo7

the talk is on Thursday

Bernardo Meurer

Crap

kim holder

1:16 AM

space tethers that rotate have to have their rotational energy restored every time they are used to lift something or land something

Bernardo Meurer

Can't we use a non-ideal board then?

kim holder

skyhooks stabilize themselves

Phase

You're a member of staff right?

Could you ask about borrowing the room of a researcher when they aren't using it? In all the universities I've been to they tend to have boards there

Very strange last resort but eh best I could come up with

0celo7

who me?

Phase

yeah

0celo7

1:21 AM

no why would I be staff

Phase

Well I mean like

PhD

Staff is a poor term

0celo7

I'm an undergrad

Phase

O

Rip

what year, out of curiosity

0celo7

that's unclear

Bernardo Meurer

@Phase He's a freshman

Phase

1:22 AM

Yeah feck off with that

Bernardo Meurer

What? It's true

Phase

If @0celo7 was the standard for undergrad freshmen I'd have offed myself

Bernardo Meurer

I am a freshman too

I'm not saying he's standard

I'm just saying he's a freshman

0celo7

@Phase you know Balarka is 14 right

Bernardo Meurer

^

Phase

1:23 AM

I cant believe either of it, it may be true but

Your both completely unreliable

Fiends you are

Trickery and deceit

0celo7

@BernardoMeurer you're a Sophomore

Bernardo Meurer

We're brothers

@0celo7 Well, technically I'm a freshman now

Phase

Ok you're pushing it too far now

Bernardo Meurer

Since I transferred

@Phase I'm not joking

Ask out sisters

Phase

>brothers

Bernardo Meurer

1:25 AM

@Phase Have you not seen us discussing thanksgiving and christmas here before?

Phase

How are families even real just close your eyes bro ha ha ha

I haven't been here long

I'm just a relatively new pleb

Bernardo Meurer

Yeah, well, now you know. Me and @0celo7 share the same father

Phase

I'll not accept it

Everything I hear here is a lie

0celo7

pretty much

even the truths are lies

Phase

Then that means that that statement is a lie

Nice paradox m8

btw is freshman a term for a new undergrad?

Bernardo Meurer

1:28 AM

Well ask anyone here and they'll confirm me and @0celo7 are indeed brothers

@bolbteppa has been here a while, am I lying?

Phase

@ACuriousMind are they?

Bernardo Meurer

@Phase First semester undergrad

Phase

Huh. Ok, I'm a Freshman then I guess

Bernardo Meurer

Or sure, @ACuriousMind confirm me and @0celo7 are brothers

@Phase Just like me and @0celo7

bolbteppa

I have never seen someone lie in here

3

Phase

1:30 AM

Being a freshman sucks

Bernardo Meurer

@bolbteppa thank you!

Phase

The most advanced thing I've done so far is gauss' law and even that's being done in a lame way

Bernardo Meurer

Go to ULisbon

I want to see you complain there

lol

Phase

Idk where that is or why it would be funny, but I'm in the UK fam

0celo7

do you know where Lisbon is?

Phase

1:32 AM

Nope

Bernardo Meurer

You don't know where Lisbon is?

Wow

oh

jeez

lol

just googled it

I've been there

:|

Bernardo Meurer

1:32 AM

That just makes it sad

0celo7

(wow)

Phase

I've been to Lisbon and Porto

Nowhere else in Portrugal tho

Bernardo Meurer

That's pretty much all of Portugal smh

Phase

Idk if I'm cut out to study physics tbh

Bernardo Meurer

It's okay to change, I changed from CEng to CS

Phase

1:35 AM

I don't wanna change though, it's practically all I enjoy aside from video games

I just can't understand some of the things I really want to, and that makes me very sad

Bernardo Meurer

Well, then you have a problem in your hands

Phase

couple that with my ability to ask totally retarded questions

and it's a cocktail of despair

Bernardo Meurer

Hm

Things are hard

Phase

I'm fine with the stuff I've encountered so far on the Syllabus its my own studies that bothers me

Bernardo Meurer

What exactly?

Phase

1:36 AM

I still haven't got god damn Diagonalising two commuting hermitian matrices entirely straight in my head

where one or both are degenerate

bolbteppa

Can you understand diagonalizing one Hermitian matrix and prove it in seconds

Bernardo Meurer

^

Phase

Yeah

bolbteppa

There is a cool way to see it

FToA then boom

0celo7

FToA?

Bernardo Meurer

1:39 AM

@Secret You should've just used Knuth's up-arrow

@0celo7 Fundamental Theorem of Algebra

Or Analysis

I imagine Algebra b/c we're talking about them bois

bolbteppa

Lets see if I remember the proof of two commuting, always forget the end

If $A$ and $B$ are simultaneously diagonalizable, then they obviously commute, $AB = BA$, however if they commute, then we can at least diagonalize one of them, say $A$, so that $a_i b_{ij} = b_{ij} a_j$ implies $(a_i - a_j)b_{ij} = 0$, so that $B$ is zero when $a_i \neq a_j$ but can be non-zero when $a_i = a_j$

Phase

Gonna be honest

Its like 2:42 and im running on low sleep, it'll be easier for me to just google this tomorrow when I'm not brain dead

bolbteppa

something something block diagonal fix eigenspaces done

Bernardo Meurer

@bolbteppa Nice and neat :)

Phase

It's just difficult applying yourself to something you have no pride in innit

Bernardo Meurer

1:44 AM

lol

Phase

I appreciate the effort though

Bernardo Meurer

@Phase What does pride have to do with this

Phase

and Im sorry for not telling you sooner, I zoned out

Maybe not pride but confidence

I have none in my ability to do physics and it leaves me a bit of a husk

innit

Bernardo Meurer

You're being a ween

Phase

ur mums a ween m8

Bernardo Meurer

1:45 AM

I agree with that

Phase

damn

bolbteppa

Nobody has any ability to do physics that's why you study it

Phase

No ability to study physics then smh whatever it is

Bernardo Meurer

@Phase You're being a ween because these things are hard for everyone

Phase

I just feel like I'm lying to myself believing otherwise

bolbteppa

1:46 AM

Only thing that matters is interest and putting the work in

Bernardo Meurer

^

@Phase I suck at maths

Like, suck

Ask anyone here who knows me

@DanielSank @ACuriousMind @0celo7

I suck at maths

Phase

I'm better at the maths than I am at the physics, but I still feel like that's not saying much. Especially compared to the calibre of the average SE user

anyhoo my apologies

Bernardo Meurer

For fucks sake who cares about "the average SE user"

Phase

This aint Counselling SE so I'll change the subject innit

Bernardo Meurer

The average SE user knows bullcrap and asks dumb questions that get flagged as duplicate

Phase

1:49 AM

Anyone found the edge of the earth yet?

ahahaha ok but

the average chat user then

Bernardo Meurer

Sure, but this is a very niche group of people

We waste our time in an online physics chatroom

Take a moment to think about that

Phase

I waste my time in Flat Earth groups too

I'm more of a lost cause

at least you people argue and talk with rational people : P

Bernardo Meurer

You expect as a freshman to come in a chatroom filled with PhDs and Grad students and so on and not feel like a moron

I'm pretty sure even the PhDs feel like a moron when @Slereah and @0celo7 talk

You just gotta stop with this imposter syndrome

You're basically watching porn and getting sad that you don't last long enough in bed

Phase

@bolbteppa also i may have been too hasty to say I can prove it in seconds, I've never written a formal proof, I usually just note that the eigenvectors are linearly independent, and that as such they form a space, where the Operator can act on. The columns of the operator can then be seen as images of the basis vectors, so given the right space the eigenvectors will be the basis vectors, and the image of them will just be the original basis vector multiplied by it's corresponding eigenvalue...

...which is the identity operator with 1's replaced with relevant eigenvalues

Ik its not rigorous, given more time I could probably write it down in actual maths

@BernardoMeurer well sure the SE chat comment was dumb but

mostly I just judge myself by my own standards rather than comparing myself to other people

bolbteppa

Whenever the eigenvalues of $A$ are equal, you isolate that part of the matrix along with that part of $B$, then re-ordering the basis so that a scalar multiple of the identity, you can change basis for this part and $A$ will always remain a multiple of the identity, so we are free to now do any change of basis on $B$, but $B$ is also Hermitian and so can be diagonalized, BOOM!

@Phase why are the eigenvectors linearly independent

Phase

1:56 AM

Ok so you separate them into block diagonals, where an n-fold degeneracy means an n by n submatrix in both of them?

oh I have to prove that too

ok

Transcript for