raptop changed the topic of #kspacademia to: https://gist.github.com/pdn4kd/164b9b85435d87afbec0c3a7e69d3e6d | Dogs are cats. Spiders are cat interferometers. | Космизм сегодня! | Document well, for tomorrow you may get mauled by a ネコバス. | <UmbralRaptor> egg|nomz|egg: generally if your eyes are dewing over, that's not the weather. | <ferram4> I shall beat my problems to death with an engineer. | We can haz pdf
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<egg|cell|egg>
UmbralRaptor: what happened in 1.6 and 1.7?
<egg|cell|egg>
Also there is a 1.7?
<egg|cell|egg>
Tensorraptop: also why the doom
<B787_300>
the DOOOOOOOOOOM egg|cell|egg
<TensorRaptop>
egg|cell|egg: so, 3 cyberdemons and a spider mastermind represent the four vector of…
<egg|cell|egg>
Meow
<TensorRaptop>
mrrrf
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TensorRaptop is now known as DeadRaptor
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<egg|cell|egg>
Tensorraptor: meow?
<egg|cell|egg>
s/r:/p:/
<galois>
egg|cell|egg meant to say: Tensorraptop: meow?
* egg|cell|egg
pokes deadraptor with a tensor
* DeadRaptor
twitches feebly.
* egg|cell|egg
pokes deadraptor with Christoffel symbol
* DeadRaptor
yelps
* egg|cell|egg
pets deadraptor
<DeadRaptor>
better, but still tired at the headache and difficulty focusing level <_<;;
<egg|cell|egg>
喵
* DeadRaptor
pets egg
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<egg|laptop|egg>
bofh: DeadRaptor: is there an analytic solution for the torque-free rotation of an arbitrary rigid body?
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<DeadRaptor>
I want to say no, if only because you can make it impossible to analytically compute the moment of inertia
<egg|laptop|egg>
assuming known moment of inertia (but general, with three distinct principal moments
<galois>
[WIKIPEDIA] Euler's equations (rigid body dynamics) | "In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with its axes fixed to the body and parallel to the body's principal axes of inertia. Their general form..."
<bofh>
hrm
<egg|laptop|egg>
bofh: feeding that with M=0 to Mathematica yields monstrosities involving JacobiSN
<egg|laptop|egg>
bofh: with the warning "Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information."
<egg|laptop|egg>
bofh: the annoying thing is that this is an ODE for ω, rather than the orientation
<bofh>
LOL did you manage to unlock Jacobi Elliptic Functions
<bofh>
congrats
<egg|laptop|egg>
bofh: i.e. for the element of 𝖘𝖔(3), not the element of SO(3)
<egg|laptop|egg>
bofh: also fun fact: KSP's Vessel class has an MOI member
<egg|laptop|egg>
which is a 3d vector
<egg|laptop|egg>
which is the diagonal of the inertia tensor about the vessel transform (that's probably the root part with its reference orientation)
<egg|laptop|egg>
bofh: of course there is no reason why the axes of that would coincide with those of the inertia ellipsoid
<egg|laptop|egg>
bofh: so they just take a random symmetric matrix, extract its diagonal, and discard off-diagonal entries :-p
<egg|laptop|egg>
the usefulness of the result is questionable
<egg|laptop|egg>
fortunately it is mostly unused by stock KSP
<bofh>
ROFL
<egg|laptop|egg>
some confused mods use it, they are probably wrong
<bofh>
UHH THAT IS NOT AT ALL A VALID MATRIX DECOMPOSITION TECHNIQUE ROFL
<bofh>
"questionable" yeah I'll bet
<egg|laptop|egg>
bofh: I mean, their sum is the trace, which *is* coordinate-free, so there's still *something* there
<bofh>
wait by random symmetric matrix do you mean literally random or is it at least based off the inertia tensor in some nebulous way?
<egg|laptop|egg>
(the trace is the sum of the principal moments)
<egg|laptop|egg>
bofh: yeah it's the inertia tensor
<egg|laptop|egg>
they just take its diagonal
<egg|laptop|egg>
but they never diagonalize it
<bofh>
yeah it turns out the "just throw away all off-diagonal entries" is *not* a valid matrix diagonalization technique
<egg|laptop|egg>
bofh: so you have something that is the vector of principal moments if the vessel axes happen to coincide with the principal axes
<egg|laptop|egg>
bofh: otherwise, it's random bullshit, but its sum is still the sum of principal moments, so there's that
<bofh>
rofl
<bofh>
this is absurd
<egg|laptop|egg>
bofh: have you seen the thing about spinning in low orbit
<egg|laptop|egg>
UmbralRaptor: bofh: "it is a classical result which dates back to Legendre and Jacobi [13] that, even in the case of three distinct moments of inertia, the flow of the free rigid body can be explicitely integrated in terms of special functions—Jacobi elliptic functions for the angular momentum equation and elliptic integrals or theta functions for the attitude equation, see e.g. [2, 32, 16, 14]."
<UmbralRaptor>
Hrm. Wikipedia's wrong, then. When was it added?
<egg|laptop|egg>
with [13] C. G. J. Jacobi. Sur la rotation d’un corps. Crelle Journal für die reine und angewandte Matematik, Bd. 39:293–350, 1849.
<egg|laptop|egg>
UmbralRaptor: which bit of wikipedia?
<egg|laptop|egg>
bofh: it uses Jacobi elliptic functions and elliptic integrals
<egg|laptop|egg>
bofh: so I guess Principia is going to have those :-p
<UmbralRaptor>
!choose Fix a radvel problem with a single line of code, the fix is cursed
<galois>
UmbralRaptor: Your options: Fix a radvel problem with a single line of code| the fix is cursed . My choice: Fix a radvel problem with a single line of code
<bofh>
elliptic integrals... I have code here somewhere that implements them. Those are more ""fun""... let me first check the paper to see which are needed, the special cases are nicer than the general ones.
<egg|laptop|egg>
bofh: Π
<egg|laptop|egg>
meow
* UmbralRaptor
eats the series
<egg|laptop|egg>
UmbralRaptor: which series
<UmbralRaptor>
egg|laptop|egg: the one you added a Π to
<egg|laptop|egg>
UmbralRaptor: I mean Π, the elliptic integral
<UmbralRaptor>
o_O
* UmbralRaptor
explodes in a shower of Bessel functions
<galois>
[WIKIPEDIA] Elliptic integral#Incomplete elliptic integral of the third kind | "In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse. They were first studied by Giulio Fagnano and Leonhard Euler (c. 1750). Modern mathematics defines an "elliptic integral" as any function f which can be expressed in the..."
<bofh>
egg|laptop|egg: oh fuck that is by far the shittiest
<egg|laptop|egg>
:D
<bofh>
F is nice, why couldn't it have been F?
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