egg changed the topic of #principia to: Logs: https://esper.irclog.whitequark.org/principia | <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…
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<queqiao--> <e​gg​> That’s 2/4
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<queqiao--> <A​Gr​il​le​dC​he​es​eS​an​dw​ic​h> egg, what method did you use to approximate trajectories in principia?
<queqiao--> <A​Gr​il​le​dC​he​es​eS​an​dw​ic​h> Id assume rk4 but i just want to see if there were any other options you considered?
<raptop> There are a bunch. see eg: https://github.com/mockingbirdnest/Principia/tree/master/integrators (and you might end up with a lecture on numerics)
<paculino> The documentation was very useful when I took a course on numerical methods
<queqiao--> <A​Gr​il​le​dC​he​es​eS​an​dw​ic​h> thank you very much!
<queqiao--> Reply to "r​ap​to​p: There are a bunch. see eg: https://github.com/mockingbirdnest/Principia/tree/master/integ...";
<queqiao--> <e​gg​> Specifically, this is the list of integration methods we have: https://github.com/mockingbirdnest/Principia/blob/master/integrators/methods.hpp
<queqiao--> <e​gg​> The integrator used for the celestial bodies is BlanesMoan2002SRKN14A by default, see https://github.com/mockingbirdnest/Principia/blob/7945353d0549e88ffd586d311524dd26c7a49f73/ksp_plugin/integrators.cpp#L46-L53.
<queqiao--> <e​gg​> In the real solar system, this is overriden to QuinlanTremaine1990Order12, see https://github.com/mockingbirdnest/Principia/blob/7945353d0549e88ffd586d311524dd26c7a49f73/astronomy/sol_numerics_blueprint.proto.txt#L7.
<queqiao--> Reply to "A​Gr​il​le​dC​he​es​eS​an​dw​ic​h: Id assume rk4 but i just want to see if there were any other options you considered?"
<queqiao--> <e​gg​> We do have RK4 in the library, under the name Kutta1901Vσ1 <https://github.com/mockingbirdnest/Princ... https://paste.gg/p/anonymous/6565fb434d9c4751aa6fde3af914a564
<queqiao--> <e​gg​> @sichelgaita Why did we add ExplicitMultistepLinearIntegrator (AdamsBashforthOrder𝑛)?
<queqiao--> <s​ic​he​lg​ai​ta​> Doing archeology, it appears that we tried many things to compute the mean equinoctial elements, including Heun, and we settled on Dormand-Prince, see https://github.com/mockingbirdnest/Principia/blame/89129e776ff86f77b96e519290b7951f54ff81e0/astronomy/orbital_elements_body.hpp#L368-L374.
<queqiao--> <e​gg​> Ah right. And we had added DormandPrince1986RK547FC earlier for the equipotentials.
<queqiao--> Reply to "A​Gr​il​le​dC​he​es​eS​an​dw​ic​h: Id assume rk4 but i just want to see if there were any other options you considered?"
<queqiao--> <e​gg​> So, Kutta1901Vσ1 (aka RK4) is not used at all in the mod, only in a test.
<queqiao--> <e​gg​> RK4 is basically never the best choice, it is just a nice thing to show in a lecture because it has a nontrivial but still smallish Butcher tableau.
<queqiao--> <e​gg​> (No relation to @Butcher.)
<queqiao--> <e​gg​> I have some graphs lying around comparing various integrators (limited to the symplectic or conjugate symplectic ones, and it only covers what we had in 2016):
<queqiao--> <e​gg​> Energy error vs. RHS evaluations on the Kepler problem with circular, Pluto, and 67P eccentricities:
<queqiao--> Reply to "e​gg​: That’s 2/4"
<queqiao--> <B​ut​ch​er​> The others are less photogenic
<queqiao--> Reply to "s​ic​he​lg​ai​ta​: Doing archeology, it appears that we tried many things to compute the mean equinoctial el..."
<queqiao--> <e​gg​> Uncharacteristically, we ended up removing Heun entirely: https://github.com/mockingbirdnest/Principia/pull/3519/commits/35612b0d9e5a403fccf2afccaa5616b01459fc7f#r1103736777
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<queqiao--> Reply to "e​gg​: Same with position error:"
<queqiao--> <s​ic​he​lg​ai​ta​> To clarify, in these graphs "left good, right bad". That's why we use QUINLAN_TREMAINE_1990_ORDER_12 when RSS is installed. (The KSP system is not stable enough for this kind of integrator.)
<queqiao--> <l​am​on​t> PVG uses DP5 now, although I don't have pretty graphs and I just used it because of popularity and ode45 in Matlab. Seems the cool kids these days use Tsit5 in Julia.
<queqiao--> <e​gg​> We don’t have ode45, looks like that’s from Dormand–Prince 1980 rather than 1986
<queqiao--> <e​gg​> (We haven’t paid much attention to the nonsymplectic integrators really, we just picked one and used it.)
<queqiao--> <l​am​on​t> is that just based on doc comments? i'd expect ode45 was DP1986 along with whatever paper it was that gave the free interpolant
<queqiao--> <l​am​on​t> did i write down what paper that was, 'cuz that was a PITA to find...
<queqiao--> <e​gg​> Hm. DormandPrince1986RK547FC is a lower_order=4, higher_order=5 method. (The 7 is the number of stages.)
<queqiao--> <e​gg​> The matlab docs for ode45 do not give the Butcher tableau.
<queqiao--> <e​gg​> DP80 A family of embedded Runge-Kutta formulae gives a method they call RK5(4)7M.
<queqiao--> <e​gg​> [DP86] A reconsideration of some embedded Runge-Kutta formulae discusses RK5(4)7FM, RK5(4)7FC, RK5(4)7FS, RK6(5)8M, RK6(5)8C, RK6(5)8S, and RK8(7)13M.
<queqiao--> <e​gg​> So indeed, we do not have ode45, we have a slightly different one.
<queqiao--> <e​gg​> The nomenclature says M is minimized error norm, S is enlarged stability region, and C is a compromise between M and S.
<queqiao--> <e​gg​> (+ is the one we picked, △ is ode45, ▽ is the one with the largest stability region.)
<queqiao--> <l​am​on​t> ah, i see. yeah, i implemented only M
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<_whitenotifier-4f63> [Principia] eggrobin opened pull request #4190: Statically link the UCRT - https://github.com/mockingbirdnest/Principia/pull/4190
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<queqiao--> <s​zy​mo​nf​.> is it possible to make principia not run at 10fps?
<queqiao--> <G​oF​or​PD​I ​(l​es​s ​dr​ag​=m​or​e ​fa​st​er​)> Get a better computer :magic: https://cdn.discordapp.com/emojis/586815068579299338.png
<queqiao--> Reply to "G​oF​or​PD​I ​(l​es​s ​dr​ag​=m​or​e ​fa​st​er​): Get a better computer :magic:"
<queqiao--> <s​zy​mo​nf​.> Thanks bro 🤓
<queqiao--> <G​oF​or​PD​I ​(l​es​s ​dr​ag​=m​or​e ​fa​st​er​)> Being serious, turn down your history and prediction length, and turn up your tolerance
<queqiao--> Reply to "G​oF​or​PD​I ​(l​es​s ​dr​ag​=m​or​e ​fa​st​er​): Being serious, turn down your history and prediction length, and turn up your tolerance"
<queqiao--> <s​zy​mo​nf​.> ❤️
<queqiao--> <G​oF​or​PD​I ​(l​es​s ​dr​ag​=m​or​e ​fa​st​er​)> These will make your trajectory less precise and extend less into the past and future, but hopefully improve your frame rate