UmbralRaptop changed the topic of #principia to: READ THE FAQ: http://goo.gl/gMZF9H; The current version is Διόφαντος. We currently target 1.3.1, and 1.4.x. <scott_manley> anyone that doubts the wisdom of retrograde bop needs to get the hell out | https://xkcd.com/323/ | <egg> calculating the influence of lamont on Pluto is a bit silly…
_whitelogger has joined #principia
UmbralRaptop has joined #principia
UmbralRaptor has quit [Ping timeout: 180 seconds]
_whitelogger has joined #principia
sdrodge_ is now known as sdrodge
bofh^28 has quit [Remote host closed the connection]
icefire has quit [Read error: Connection reset by peer]
<novasilisko>
"bifurcation point" in the video means the point where you can get two acceptable equillibrium states, not neccessarily one or the other
<novasilisko>
although oblate spheroids seem to eventually give way to triaxial ellipsoids
<novasilisko>
the worst thing about this is on the surface, you wouldn't know
<novasilisko>
the "apparent" gravitational force would still be perpendicular to the surface across the whole thing
<novasilisko>
(if it truly is in hydrostatic equilibrium)
<novasilisko>
your amazement and disbelief is exactly why i'm pursuing this >:v
<novasilisko>
i yearn for the "wtf is that" response!
<novasilisko>
althoouughh to get the gravitation more correct, @egg would need to help me figure out gravitation on an oblate body
<novasilisko>
i dunno whether it would make you more willing to help or more willing to hit me with a stick if i said it's okay to assume one of uniform density
<egg>
WTF is this poincaré surface Ꙩ_ꙩ
<novasilisko>
right?
<novasilisko>
i probably won't implement that, gotta say
<egg>
novasilisko: well, uniform density would make things easier, but bofh is probably more competent when it comes to turning something to spherical harmonics
<bofh>
I'm kind of just staring at this poincaré surface and going what the hell.
<novasilisko>
imagine having a planet like that in the solar system
<novasilisko>
or, hell, living on one
<bofh>
like, uniform density would def. be the approximation I'd first attempt even tho it looks incorrect from that animation
<egg>
bofh: well, I don't know what assumptions that animation uses
<novasilisko>
like i said, i'm not gonna touch the poincare pear
<egg>
bofh: maybe it simulates a fluid of uniform density
<egg>
novasilisko: but it's cute
<novasilisko>
ellipsoids are as far as i go
<egg>
but yes, the triaxial ellipsoid is already funky
<bofh>
18:02:11 <@egg> but yes, the triaxial ellipsoid is already funky
<bofh>
the triaxial ellpsoid is giving me a slight headache in thinking how to decompose it in terms of spherical harmonics
<bofh>
like that looks like an absolutely atrocious decomposition.
<novasilisko>
stuff i've found so far has either been a wall of formulae that makes me want to hide, or just saying "the only way is an iterative solution"
<novasilisko>
and i already kinda made an iterative solution which basically treats it like a mesh and checks the planes of triangles formed by vertices
<novasilisko>
but that's obviously lumpy unless i have a humungous amount of samples
<novasilisko>
now i'm totally okay with an iterative solution, but something that involves something not quite as leadpipe-y as sampling thousands of vertices/triangles
<novasilisko>
i swear i've heard "leadpipe" used as a synonym for a brute force programming solution before but have no idea where
<bofh>
18:13:05 < novasilisko> and i already kinda made an iterative solution which basically treats it like a mesh and checks the planes of triangles formed by vertices
<bofh>
I mean decomposing it into a Bézier Mesh is *a* solution, & prolly the computationally easiest one I think
<bofh>
But it's kind of unsatisfying from a physical accuracy PoV
<novasilisko>
yeahhh... i was experimenting with it, there's points where the altitude will start going down then back up again as it hits a corner of the mesh, for instance, which is bleh
icefire has joined #principia
UmbralRaptop has joined #principia
<novasilisko>
it kind of spooks me that other solutions would be -more- expensive than checking a thousand triangles
xShadowx|2 has joined #principia
xShadowx has quit [Ping timeout: 190 seconds]
<novasilisko>
something is really confusing me from that page i linked
<novasilisko>
"The maximum rotational speed is reached when the radius is only about 20% larger than the current radius. This speed is then about 11 times the current speed, so that our days at this point would last 2 hours and 8 minutes! Beyond that point, the days will get longer again, as the speed decreases. However, we may not notice as now the Earth is get
<novasilisko>
ting flat, and depending on where we are on the globe, the sun may never set or never rise.."
<novasilisko>
i can't work out what it's trying to say
<novasilisko>
is it saying the tangential velocity reaches a peak, or the rotation period, or something else?
<novasilisko>
neither of those seem like they'd be true
<novasilisko>
my first assumption would be that the faster you spin it, the flatter it gets and the higher the tangential velocity
<bofh>
I *think* the tangential velocity *should* reach a peak at some point, but I'm not sure if that's the right interpretation there. Augh.
<bofh>
LOL
<novasilisko>
imagine trying to disprove those damn flat earthers on THAT planet
<novasilisko>
but yeah, like... if you increase the rotation rate, and increasing the rotation rate increases the equatorial radius, one would assume the equatorial tangential velocity would increase in step with that
<bofh>
It should, yeah.
<novasilisko>
MacLaurin shows that, as the angular momentum increases, the Earth will get ever more flat. The shape is an ellipsoid with two equal axes, rotating around the short axis. The ellipsoid becomes a disc with an ever increasing radius. The rotation speed first increases, but the speed reaches a maximum and will then decrease. As the radius of the disc
<novasilisko>
must go to zero for a finite L and an ever increasing radius.
<novasilisko>
continues to grow and tends toward infinity, the rotation speed will tend toward zero: L can be expressed as L=ω.I, where I is the moment of inertia. For a constant mass, the moment of inertia of any object will get larger and larger as the object takes on a shape where a radial dimension becomes larger and larger. Therefore the rotation speed ω
<novasilisko>
huh.
<novasilisko>
okay, so that's based on angular momentum
<GregroxMun>
so we're not just spinning it up
<novasilisko>
if you keep increasing rotation rate, it sure will keep flattening - and then fly apart
<GregroxMun>
we're increasing momentum
<GregroxMun>
this makes sense, too, as the maclaurin spheroid does have an upper stability limit
<novasilisko>
shit's weird
<GregroxMun>
for angular velocity
<GregroxMun>
but apparently NOT for angular momentum
<bees>
force planet makers to provide their own custom geometry for planets?
<bees>
this way it would not be _your_ headache
<novasilisko>
you incorrectly assume i am working with KSP!
<novasilisko>
this is my, self-induced headache
<novasilisko>
and that was my, unnecessary comma
<bees>
then compute some kind of cache and just read it?
<novasilisko>
i mean, the current method is to store vertex and triangle data and iterate that like i mentioned earlier so i guess i already am?
<bees>
not accurate enough for desired accuracy?
<bees>
*fast
<novasilisko>
yeah, it gets slow quickly unfortunately, and decreasing it enough that it's fast means it's lumpy, you hit peaks and troughs so to speak
<bees>
can you use a different function for low speed/low altitude travel?
<bees>
if you know nearby triangles position already
<bees>
maybe you could approximate very low curvature very fast if you drop a tiiiiny bit of accuracy
<bees>
something simular with KSP model, where when you drop below a certain height, you get terrain, otherwise it is not even modeled (i think)
<bees>
in your case, you have a sharp relatively big triangles, that you can smooth out somehow if you are close enough for it to be relevant
egg|work|egg has quit [Quit: webchat.esper.net]
<novasilisko>
i think i can make the triangle approximation work, this has mainly been a quest of "There's Got To Be A Better Way"
<novasilisko>
because it just feels so damn wrong, you know?
<egg>
yeah, there likely is a better way
<egg>
try poking bofh, or i might have time eventually
<novasilisko>
i accidentally distracted him with the poincare pear last time
<egg>
novasilisko: keep poking, sometimes it works
<egg>
novasilisko: just be careful, bofh's "sec" can be long
<novasilisko>
this was his take last time
<novasilisko>
"the triaxial ellpsoid is giving me a slight headache in thinking how to decompose it in terms of spherical harmonics
<novasilisko>
like that looks like an absolutely atrocious decomposition. "
<novasilisko>
"I mean decomposing it into a Bézier Mesh is *a* solution, & prolly the computationally easiest one I think
<novasilisko>
But it's kind of unsatisfying from a physical accuracy PoV "
<novasilisko>
it's so frustrating :v i was hoping for, i don't know, Mendyvort's Ellipsoidal Distance Theorem to be dropped in my lap and solve everything
<egg>
novasilisko: no but that's because i nerd-sniped him in a different direction
<egg>
novasilisko: namely the gravity model
NoSyk has quit [Ping timeout: 190 seconds]
<egg>
novasilisko: but that's not what you're looking for for the geometric problem
NolanSyKinsley has joined #principia
<novasilisko>
mm
<egg>
also re. triaxial ellipsoid spherical harmonics, you can probably get a good approximation with the C20 C22 S22 terms; not sure how you fit them to the ellipsoid, I'd have to look how you do that for C20 to a revolution ellipsoid
<egg>
it's defined in some IAU/IAG report iirc
<novasilisko>
it's been tough to find what i want for the gravitation cause it's usually buried in earth-centric stuff
<novasilisko>
i have had a lot of trouble finding something general
<novasilisko>
though, the geometric part is still the priority
<novasilisko>
is it too sinful to just assume a uniform density with no mascons or anything
<egg>
novasilisko: even then you'll have to represent the ellipsoidiness somehow
<egg>
and somehow is through a geopotential model
<egg>
except you can probably get away with three terms
<egg>
instead of hundreds like on the moon or something :-p
<novasilisko>
well that's something at least
<novasilisko>
i at least know i can assume the two are in the same reference frame
<novasilisko>
i have a sincerely very difficult time, i might have said before, translating between like, speaking language<->mathematical language<->programming language
<novasilisko>
always have had a tough time explaining things i've programmed or programming things based on written ideas for instance, have to pretty much think in code
<novasilisko>
all of which kinda makes me feel like an outsider around here
<novasilisko>
which i guess i am, having only been in here for like a day
<bees>
hmmmm
<bees>
how would a planet core look like for this pancake
<novasilisko>
i would really like to 100% ignore differentiation in the interior to be honest, the difference between that and the real numbers are not significant enough to matter for my purposes
<novasilisko>
yet,a nnoyingly, are different enough from just calculating a point source to matter
<novasilisko>
i'm running out of mental energy here, this shit is getting stressful fast
<novasilisko>
i'm never smart enough to get ahold on these things
NolanSyKinsley has quit [Ping timeout: 190 seconds]
NolanSyKinsley has joined #principia
NoSyk has joined #principia
NolanSyKinsley has quit [Ping timeout: 190 seconds]
kmath has quit [Ping timeout: 202 seconds]
Mike` has quit [Ping timeout: 202 seconds]
Mike` has joined #principia
xShadowx has joined #principia
xShadowx|2 has quit [Ping timeout: 183 seconds]
paco__ has joined #principia
NoSyk has quit [Remote host closed the connection]
paco__ has quit [Remote host closed the connection]
NoSyk has joined #principia
NoSyk has quit [Remote host closed the connection]