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Q: Roughly how many kinds of closed or periodic orbits are there in the circular restricted three-body problem?

10:19 AM

I never understood English's obsession with weird collective nouns but it's neat it even has ones for mathematical objects :P

JingleBells

I am a math object

Emilio Pisanty

@CaptainBohemian I was just joking, but it seems I wasn't too far off

I was just making fun of the English language

3 hours later…

Captain Bohemian

1:36 PM

@JohnRennie I use foliage for this.

@ACuriousMind isn't audience a collective noun, either? Why I saw a naive reader in a writing guide?

uhoh

1:56 PM

Question: Roughly how many kinds of closed or periodic orbits are there in the circular restricted three-body problem? Has anyone made an attempt to enumerate and classify/categorize them? Notes: If there is a distinction between closed and periodic required to answer the question, you can choose...

I've added a bounty

1 hour later…

JingleBells

3:08 PM

In terms of validating assumptions regarding a business idea or specific features, after I've gathered customer behaviour and feedback data, how do I determine the threshold of success or failure of validating or disproving the given assumption?

Simply said, if I'm tracking a sign up button, what number am I aiming for regarding the ratio of button clicks to page views?

@EmilioPisanty Home is where the heart is.

Hello everyone!

I wrote a program on solving Newton's law of motion, and was playing around with different arbitrary potentials and giving random initial values to check out their trajectories,I got a few very interesting cases like this.

Do you know where I can find more potentials,which produces such nice trajectories?

what are the axes?

@ZeroTheHero 2D cartesian

but not like position and velocity...

you have some sort of central potential and you're plotting the position x,y in the plane.

3:16 PM

@ZeroTheHero yes

@ZeroTheHero I drew some phase space trajectories too.

I want to know about more such potentials which give beautiful trajectories as these.

Potential maybe time dependent/velocity dependent,anything..

there are some nice trajectories for the 3-body problem in the plane.

yes it's called the restricted 3-body problem.

@ZeroTheHero I drew some Lorenz attractor plots(x-z plane) like this but I don't think you mean exactly that?

JingleBells

Pff and as always my business questions where ignored, not surprising since this is a shysics chatroom

3:24 PM

@ManasDogra see Borcherds, P.H., 1996. The restricted gravitational three-body problem trajectories associated with Lagrange fixed points. European Journal of Physics, 17(2), p.63.

some of resulting trajectories are quite neat.

@ZeroTheHero :( I could see if I had an access.

Charlie

Just been told I did well enough in my grad diploma to likely be given a place on a master's in physics, the dream is alive for at least another year :D

woo

yay

@ZeroTheHero wow!

3:40 PM

yes some of the orbits go 'round one body, then "transfer" to the other body, and then quasi-escape but come back.

@ManasDogra anyways... have to go. 'have fun.

1 hour later…

4:59 PM

3 messages deleted

Charlie

lmao

@JingleBells You've been told plenty of times not to spam the chat with nonsense. Since just telling you doesn't seem to have any effect, I've suspended you from chat for an hour. It will be longer next time.

5:18 PM

hello

greetings

I'm trying to derive the equations of motion for a pendulum with friction basically.

I did the simple pendulum

but it doesn't dissipate so my python code goes on forever

I have the final equation for the one with friction

but i can't seemed to find anything that tells me what the force actually looks like geometrically

most pictures just don't show it

so i'm having trouble visualizing what is creating the friction

and where i would put it in my free body diagram

@StanShunpike There's plenty things contributing to the energy of the pendulum dissipating, but what's wrong with just taking air friction as a first approximation?

@ACuriousMind that makes sense, but at what point do i include it? Would this be something I would write

$\frac{d}{dt} \left(\frac{\partial L}{\partial \dot{\theta}}\right) - \frac{\partial L}{\partial \theta} = F_{friction}$

Lagrangian/Hamiltonian formalisms don't do well with friction

5:24 PM

oh interesting

why not?

First, see physics.stackexchange.com/a/147348/50583 by Qmechanic for how to do Lagrangian mechanics with friction - his "canonical approach" is basically what you suggest

Second, they don't do well with friction because friction is path-dependent and hence has no potential, but the Lagrangian/Hamiltonian is usually thought of as the kinetic energy term plus a bunch of potential terms

So you don't have anything for friction that you can write into the Lagrangian to get friction in the e.o.m., and you have to do a hack and include it by hand

wow that's super interesting. I did not know that. Thanks very much! that was super helpful :)

his answer is great

they all are ;P