egg|zzz|egg changed the topic of #principia to: READ THE FAQ: http://goo.gl/gMZF9H; The current version is Coxeter. We currently target 1.2.2, 1.3.1, and 1.4.1. <scott_manley> anyone that doubts the wisdom of retrograde bop needs to get the hell out | https://xkcd.com/323/
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<GH>
Principia/master 76c05ed pleroy: The old tests pass.
<GH>
Principia/master d8ad241 pleroy: An implementation that compiles.
<GH>
Principia/master d08eab8 pleroy: Start to write a test.
<GH>
[Principia] pleroy opened pull request #1803: Support for Gipfeli in the plugin and in C# (master...Gipfeli3) https://git.io/vpBc1
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<GregroxMun>
I have come in search of smart people
<GregroxMun>
not people who demand integrators
<GregroxMun>
for I need help of the keplerian kind
<GregroxMun>
a friend and I are working on a game and we need to simulate orbital mechanics. We do *not* need anything n-body, we essentially need to replicate KSP's on-rails planet system, just input the keplerian elements and output the position of the object.
<GregroxMun>
at the moment, it seems to have swapped the behavior of eccentric orbits
<GregroxMun>
the planet goes faster at apoapsis than at periapsis.
<GregroxMun>
egg?
<egg|phone|egg>
UmbralRaptor
* egg|phone|egg
zzz
<GregroxMun>
UmbralRaptop?
<UmbralRaptop>
ping
<GregroxMun>
can you help?
<UmbralRaptop>
I think so.
<GregroxMun>
so we need to calculate true anomaly based on time, semimajor axis, and eccentricity
* UmbralRaptop
pre-emptively stabs the Kepler equation.
<GregroxMun>
we got kepler's law 1 and 3 but we're missing number 2
<UmbralRaptop>
I'm half-expecting that there's a sign error.
<GregroxMun>
so it isn't actually just flipping the focus
<GregroxMun>
this isn't a bug, it just isn't well done yet
<GregroxMun>
the problem is right now we fling the planet along the elliptical path from the point of view of the focus at a constant angular rate
<GregroxMun>
just sweeping it linearly based on time
<GregroxMun>
I can show you a gif
<UmbralRaptop>
Basically acting as if mean anomaly is real?
<GregroxMun>
but it shouldn't be important
<GregroxMun>
yeah
<UmbralRaptop>
The classical approach is to find eccentric anomaly from mean anomaly, and then true anomaly from that. The first step is annoying.
<GregroxMun>
right
<GregroxMun>
we've seen that this apparently requires you to iterate
<GregroxMun>
but that doesn't seem right for something you should be able to do continuously
<UmbralRaptop>
You could probably do something like cut off after a limited number of iterations or size of changes in eccentric anomaly.
<GregroxMun>
how well would that work for something done in real time?
<GregroxMun>
ok he found something and wants to know if this is fucked up
<UmbralRaptop>
I think this ends up depending on lots of assumptions about precision.
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<UmbralRaptop>
Is that a 1st order Taylor expansion?
<GregroxMun>
of course I know what a taylor expansion is, but just in case there's someone else in the channel who doesn't, why don't you give them a refresher
<UmbralRaptop>
The idea is to convert a function to a power series via f(x) = f(a)/0! + f'(a)*(x-a)/1! + f''(a)*(x-a)²/2! +…
<UmbralRaptop>
where a is some constant you want to center the series at. 0 is popular.
<UmbralRaptop>
Hrm, apparently this is doing something different.
* UmbralRaptop
wonders if there's some Fourier weirdness.
<UmbralRaptop>
Anyway, that formula has problems at higher eccentricities.
<UmbralRaptop>
I'm going to go with "it's clever, but several iterations of Newton's method should beat it for e near 1. (For low e, it doesn't matter much)
<GregroxMun>
thanks
<UmbralRaptop>
egg|anbo|egg would know how to do a better comparison, but that should hold.