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The source code is available on GitHub under the MIT license. Abstract This mod aims to replace KSP's unstable physics integration with a higher-order symplectic integrator, adding n-body Newtonian gravitation in the process. Acronyms Documentation and download Principia is not built in the same way as most other mods (most of it is native code, with a thin C# interface layer), so that compatibility issues may arise depending on the platform. Binaries are available for Windows, Linux (built on Ubuntu, your mileage may vary when using these on other distributions), and Macintosh (thanks to @Jim DiGriz). Note that the mod only works with 64-bit versions of KSP. Please read the wiki page detailing the concepts carefully; a lot of things behave differently when using principia, in particular map view and flight planning. Many aspects of the mod are unfinished, and this is detailed on that page. In addition, please read the FAQ and bug reporting guide. Note that bug reporting procedures differ significantly from those of other mods because of our custom logging system, our use of fatal failures, and our journalling system (which, if activated, allows us to replay the events that led to a crash for later debugging). A tutorial is available on the topic of going to the Mun in various ways, applying the concepts described above. There is also a guide to low orbit rendezvous that should help with understanding the target LVLH frame. Since Principia makes all bodies attract each other according to Newtonian gravitation, the stability of the solar system is a concern; when using stock KSP, Principia modifies the Jool system so that it is stable. When using a customized system (e.g. with Kopernicus), you need to make sure that the system is stable. If you wish to ask questions or report bugs, you may want to do so on IRC (on the #principia IRC channel on EsperNet). Your concerns may be addressed more quickly there than on the fora (bear in mind however that there isn't always someone around who can answer your question right away; if no-one is around, you may want to stay on the channel for a while). Download the binary (Macintosh, Ubuntu, and Windows): Principia Fuchs for 1.5.1, 1.6.1, and 1.7.3, Principia Fuchs for 1.8.1 and 1.9.1; or from 腾讯微云: Principia Fuchs for 1.5.1, 1.6.1, and 1.7.3, Principia Fuchs for 1.8.1 and 1.9.1. Alternatively, if you don't trust our binary, build the mod from the Fuchs release. We provide a patch to turn @GregroxMun's SLIPPIST-1 into the TRAPPIST-1 system; see the installations instructions. Status Dates are ISO 8601 extended format. 2020-05-22 For the new moon (lunation number 252), the new release (Fuchs) is out. The issues with rotation (uncontrolled spin-up, jerky motion, oscillations, etc.) introduced in Frobenius and Fubini have for the most part been solved. We are aware of one remaining case of aberrant spin-up, reported by @scimas, but this seems to be a very rare issue at this point. Prior to ignition, the manœuvre node marker on the navball for guided burns now points to the orientation at ignition, instead of following the current Frenet frame. This is more useful for manual burns (the spacecraft can be oriented correctly prior to ignition, instead of having to be guided even before the manœuvre starts). Perhaps more importantly, in conjunction with change MuMech/MechJeb2#1264 (available in MechJeb dev builds ≥ 958), this means that MechJeb can execute all Principia manœuvres. New APIs have been added for use by @Sir Mortimer’s KerbalismContracts. See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.9.1 & 1.8.1, and for 1.5.1, 1.6.1, 1.7.x. Make sure you download the right one (if you don't, the game will crash on load). For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. This is the last release to support KSP 1.5.1, 1.6.1, and 1.7.x, as Realism Overhaul and Real Solar System now support 1.8.1. 2020-04-23 For the new moon (lunation number 251), the new release (Fubini) is out. Support for 1.9.1 has been added. The flight planning and orbit analysis window are now available in the tracking station, bringing into line with map view. Some changes have been made to mitigate the aforementioned issue #2519. Wild spin no longer seems to be an issue, however some unexpected oscillations arise under some circumstances. We will keep investigating this issue. Some issues that would cause crashes have been resolved. See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.9.1 & 1.8.1, and for 1.5.1, 1.6.1, 1.7.x. Make sure you download the right one (if you don't, the game will crash on load). For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2020-03-24 For the new moon (lunation number 250), the new release (Frobenius) is out. After nearly a year of work and 96 pull requests, Principia now enforces the conservation of angular momentum, as had been alluded to earlier. This means, among other things, that: the long-standing bug #1639, reported by @Damien212 in 2017, whereby the orientation of vessels changed when they underwent an SoI transition, is resolved; vessels will rotate as rigid bodies, following Euler’s equations, in time warp; in particular they may exhibit the Джанибеков effect in time warp, as illustrated in the short video below; changes in mass distribution within the vessel, e.g., due to fuel transfer, will affect the angular velocity, as illustrated in the short video below. See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.8.1, and for 1.5.1, 1.6.1, 1.7.x. Make sure you download the right one (if you don't, the game will crash on load). For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2020-02-23 For the new moon (lunation number 249), the new release (Frenet) is out. Nothing new this time; we have been working on the preservation of angular momentum, but it is not quite ready yet. See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.8.1, and for 1.5.1, 1.6.1, 1.7.x. Make sure you download the right one (if you don't, the game will crash on load). For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2020-01-24 For the new moon (lunation number 248), the new release (Frege) is out. Celestial histories are now displayed as far as requested in the past (if available), rather than being limited to the time of launch. Miscellaneous bugs have been fixed (perhaps most visibly, the wild camera spin in the pause menu introduced in Fréchet).  See the change log for more details; note in particular the known issue with map view camera rotation when showing the menu. We support two sets of versions of KSP: downloads are available for 1.8.1, and for 1.5.1, 1.6.1, 1.7.x. Make sure you download the right one (if you don't, the game will crash on load). For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2019-12-26 For the new moon (lunation number 247), the new release (Fréchet) is out. Support for KSP 1.8.1 has been added. The camera is oriented in map view and the tracking station so that the horizontal is the reference plane of the selected plotting frame. Further, the camera rotates with the plotting frame, so that the plotted trajectories do not rotate as time passes.  See the change log for more details; note in particular the known issue with map view camera rotation when showing the menu. We support two sets of versions of KSP: downloads are available for 1.8.1, and for 1.5.1, 1.6.1, 1.7.x. Make sure you download the right one (if you don't, the game will crash on load). For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2019-11-26 For the new moon (lunation number 246), the new release (פרנקל) is out. Principia now plots the trajectories of celestial bodies. This closes an ancient feature request (#942, March 2016), and builds up on a lot of intervening work; in particular, this is based on the method for trajectory plotting introduced for vessels in Чебышёв (August 2017). The history length setting now hides the history instead of forgetting it; this means that you can shorten histories when they are visually distracting, while retaining the ability to bring them back when you want an overview of your mission. It also uses the same duration format and selector used elsewhere in the Principia UI instead of seconds in scientific notation.  See the change log for more details. For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2019-10-28 For the new moon (lunation number 245), the new release (Fourier) is out. Two crashes involving flight plan edition (one reported by @Neph) have been fixed.  See the change log for more details. For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云 2019-09-28 For the new moon (lunation number 244), the new release (Fibonacci) is out. An orbit analysis tool has been added which computes mean elements and orbit recurrence properties. This has been in the works since February; more features will be added at a later date, e.g., mean solar times of ascending nodes (for controlling sun-synchronicity). See below for a screenshot of the orbit analysis tool in action on a Молния orbit. The tool is fairly complex; documentation will be provided soon. A crash reported by @Delay has been fixed. A dependency issue that would prevent Principia from starting has been fixed.  See the change log for more details. For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2019-08-30 For the new moon (lunation number 243), the new release (del Ferro) is out. Higher degree and order gravity models have been added for Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune; satellites of these planets will now have more realistic motion (this change only takes effect on new saves) Some bugs reported by @Sir Mortimer, @scimas, and @Kobymaru have been fixed.  See the change log for more details. For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2019-08-01 For the new moon (lunation number 242), the new release (Ferrari) is out.  Support for KSP 1.7.3 has been added. Some bugs reported by @scimas have been fixed.  See the change log for more details. For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2019-07-02 For the new moon (lunation number 241), the new release (Fermat) is out. Support for KSP 1.7.1 and 1.7.2 has been added; as previously announced, this release does not support KSP 1.3.1 and 1.4.x. A long-standing feature request (#1936, opened by @王小谦同学) has been addressed: all manœuvres of a flight plan can be edited, instead of only the last one. Manœuvres now take the thrust limiter into account (#2128, opened by @Kinexity). See the change log for more details. For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2019-06-03 For the new moon (lunation number 240), the new release (Fatou) is out. Support for KSP 1.7.0 has been added. Note that 1.7.1 was released after we built the release, so it is not supported. Also note that we have no special support for the new orbital information display, so that, like MechJeb or Kerbal Engineer Redux, it will display the largely-useless osculating elements at current time instead of mean elements for some appropriate theory. Further, note that we have no special support for the new manœuvre node editor, so that it will likely be unusable. This is the last version to support KSP 1.3.1 and 1.4.x, as Realism Overhaul and Real Solar System now support 1.6.1. The next version will only support 1.5.1 and up. The ascending and descending nodes are now shown with respect to the equator in the body-centred, body-fixed frame, and in the body-centred inertial frame if the central body is sufficiently close (#1841). Many bugs have been fixed that were introduced with the UI changes in Fáry and during the underlying restructuring of the UI code in Fano. See the change log for more details. We thank @Miracle Magician for reporting a severe bug that would otherwise have been introduced in this release. We support two sets of versions of KSP: downloads are available for 1.4.x, 1.5.1, 1.6.1, 1.7.0, and for 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). For the convenience of our Chinese users, the binaries can be downloaded either from Google Drive or from 腾讯微云. 2019-05-04 For the new moon (lunation number 239), the new release (Fáry) is out. The UI now scales according to the KSP UI scale settings, and has been made a little more compact; those flight plan settings that are controlled by a slider can now also be edited by text entry (this includes the Δv components and timing of manœuvres); the TRAPPIST-1 patch has been updated for @GregroxMun’s SLIPPIST-1 v0.7.x.  See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.4.x, 1.5.1, & 1.6.1, and for 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2019-04-05 For the new moon (lunation number 238), the new release (Fano) is out. The predictions are now computed asynchronously, making long predictions usable; this is particularly noticeable in the vicinity of bodies with complex gravity models, such as the Earth and Moon in RSS. Some bugs involving map view markers have been fixed. See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.4.x, 1.5.1, & 1.6.1, and for 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2019-03-06  For the new moon (lunation number 237), the new release (Euler) is out. Issue #2072, introduced in Erdős, which manifested as free fall unaffected by parachutes or engines below 8.4 m altitude in RealSolarSystem (leading to rough splashdowns), has been resolved. An API has been added to allow @Jim DiGriz’s guidance algorithms to access the geopotential coefficients; see #2074. See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.4.x, 1.5.1, & 1.6.1, and for 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2019-02-04  For the new moon (lunation number 236), the new release (Εὐκλείδης) is out. Support for KSP 1.6.1 has been added. This release fixes a long-standing issue (reported in November 2017 by @Agustin, in June 2018 on GitHub as #1868 by @scimas, and by @Delay in January 2018) where, under some circumstances, the SAS would not point the ship towards the markers (it would point the ship towards the position that the markers would have in stock instead). It also fixes a relatively rare issue involving fragments of vessels getting close to the centre of a celestial on reentry (#2056). See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.4.x, 1.5.1, & 1.6.1, and for 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2019-01-06 For the new moon (lunation number 235, partial eclipse), the new release (Εὔδοξος) is out. We have added an enhanced selenopotential in RSS, complete to degree and order 30; this means that the moon now has mascons, making some low lunar orbits unstable. Note that you will only get the new selenopotential when making a new save. As a concrete example, consider this screenshot of a lunar orbit, whose periapsis decreases by 3400 m over the course of 18 orbits because of the irregularities of the Moon's gravitational field (another dozen orbits later, the spacecraft collides with the Moon, between craters Spencer Jones and Spencer Jones W). Saves are now encoded in base64 instead of hexadecimal, making them smaller and faster to load. We have rerun the TRAPPIST-1 optimization, this time with a small enough integration time step allowing us to accurately model the dynamics of the system. Thanks to @AloE for spotting the incorrectly-timed transits. The resulting system has residuals similar to those reported by Grimm et al., with χ² = 358.79 vs. χ² = 342.29 in the paper. See the change log for more details. We support two sets of versions of KSP: downloads are available for 1.4.x & 1.5.1, and for 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2018-12-07 For the new moon (lunation number 234), the new release (Erdős) is out. Support for realistic geopotential modeling at arbitrary degrees is finally available, with a 10th-degree model of the Earth geopotential in RealSolarSystem; more advanced modelling for other bodies (Moon, Mars, etc.) will be added in future versions. #1955, a performance issue on macOS (continuation of #1908), was resolved by using a different synchronization library. The issue reported by @AloE above (#1999) has been temporarily addressed by using the same integrator configuration that was used for the optimization. We will redo the optimization with a more appropriate configuration in a future version, as this issue likely indicates that the integrator had not quite converged. see the change log for more details.  We support two sets of versions of KSP: downloads are available for 1.4.X & 1.5.1, and for 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2018-11-07 For the new moon (lunation number 233), the new release (Ἐρατοσθένης) is out. Support for KSP 1.5.1 has been added. We working on extending geopotential models beyonds oblateness (mascons etc.), but that is not yet ready; see the change log for more details.  We support two sets of versions of KSP: downloads are available for 1.4.x & 1.5.1, and for 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2018-10-09 For the new moon (lunation number 232), the new release (Διόφαντος) is out. Nothing new this time; we have been working on improved gravity models, but they are not ready yet. See the change log for more details.  We support two versions of KSP: downloads are available for 1.4.5 and 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2018-09-09 For the new moon (lunation number 231), the new release (Descartes) is out. Important note for mac users: Principia no longer supports macOS El Capitan, as that version is no longer supported by Apple. We now require macOS Sierra or later. As a consequence, there should be noticeable performance improvements for macOS users. We have added generalized Runge-Kutta-Nyström methods, which allow for a more accurate prediction of burns that are fixed in the Frenet frame. See the change log for more details.  We support two versions of KSP: downloads are available for 1.4.5 and 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2018-08-11 For the new moon (lunation number 230), the new release (Desargues) is out. No new features in this version beyond the 1.4.5 upgrade, as we have been on vacation.  See the change log for more details.  We support two versions of KSP: downloads are available for 1.4.5 and 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2018-07-13 For the new moon (lunation number 229), the new release (Δημόκριτος) is out. Vessels are now managed by Principia when they are in the atmosphere, which means that atmospheric flights have Principia histories and predictions in map view. The “Trappist-1 for Principia” mini-mod has been improved to better reflect the physical properties of the celestials. See the change log for more details. We support two versions of KSP: downloads are available for 1.4.4 and 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2018-06-12 For the new moon (lunation number 228), the new release (Dedekind) is out. This release fixes a memory leak which could lead to increases in memory usage to the tune of 1 GiB / min when using the flight plan. Further, we are releasing a mini-mod that turns @GregroxMun's SLIPPIST-1 into the real TRAPPIST-1 system; the 7-planet resonant chain of that system makes it interesting from the perspective of n-body gravitation. The configuration is computed by transit-timing variation based on the transit timings from the recently-published paper The nature of the TRAPPIST-1 exoplanets by Grimm et al. See the change log for more details. We support two versions of KSP: downloads are available for 1.4.3 and 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). 2018-05-15 For the new moon (lunation number 227), the new release (Darboux) is out. This release: uses a new implementation of the cube root which is more accurate and faster than most, as part of an ongoing effort for Principia to use its own implementation of elementary functions; adds Gipfeli compression and arena allocation when saving and loading, reducing save file size by about 2.5× and scene load times by about 2× for large saves; adds support for KSP 1.4.3. See the change log for more details. We support two versions of KSP: downloads are available for 1.4.3 and 1.3.1. Make sure you download the right one (if you don't, the game will crash on load). Darboux does not support KSP 1.2.2, as Realism Overhaul and Real Solar System now support 1.3.1. 2018-04-16 For the new moon (lunation number 226), the new release (Cramer) is out. This release: fixes a bug which caused manoeuvre nodes to jump at the time of ignition, especially on ejection and capture burns. Thanks to @Kobymaru and @EstrelaGaliza for reporting and helping diagnose this bug. adds support for KSP 1.4.2. Note that you may need to install a newer C++ runtime; see the change log for more details. We support three versions of KSP: downloads are available for 1.4.2, 1.3.1, and 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). Cramer will not support 1.4.3, as Principia has special handling to work around ladder-related bugs, so we will need to test the new release to see if changes are needed. This is the last release to support KSP 1.2.2, as Realism Overhaul and Real Solar System now support 1.3.1. 2018-03-17 For the new moon (lunation number 225), the new release (Coxeter) is out. This release: uses SSE2 intrinsics for improved performance; addresses numerical stability issues in the Jool system reported by @Eriksonn; introduces an API for @Jim DiGriz's guidance algorithms; introduces support for KSP 1.4.1, thanks to @awang. See the change log for more details. We support three versions of KSP: downloads are available for 1.4.1, 1.3.1, and 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). 2018-02-15 For the new moon (lunation number 224), the new release (Cohen) is out. The ephemerides are now computed using the Estrin method for polynomials expressed in the monomial basis instead of the Clenshaw method for polynomials expressed in the Чебышёв basis, improving the performance. See the change log for more details. Again, we support two versions of KSP: downloads are available for 1.3.1 and for 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). 2018-01-17 For the new moon (lunation number 223), the new release (Clifford) is out. A bug in the implementation of DoublePrecision that caused a test to fail on Macintosh, as reported by @awang and @Jim DiGriz, was fixed. Solar system designers can now pick an integrator more suited to their solar system, as requested by @GregoxMun whose surprisingly stable Alternis Kerbol Rekerjiggered does not fare well with Principia's default integration parameters, which were chosen (in Cartan) to work for stock KSP and the real solar system. See the change log for more details. Again, we support two versions of KSP: downloads are available for 1.3.1 and for 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). Thanks to @awang for contributions (clang warning cleanups) during this lunation. 2017-12-18 For the new moon (lunation number 222), the new release (Christoffel) is out. Vessels no longer pass through a planet unharmed at sufficiently high timewarp like in stock, and are detected by Principia as having collided with the planet, and are destroyed. In particular, this resolves the crash that occurred in 陈景润 when a vessel went through a planet unscathed (#1628, reported by @awang and @John FX). Support for KSP 1.3.0 has been dropped. We support two versions of KSP: downloads are available for 1.3.1 and for 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). See the change log for more details. 2017-11-18 For the new moon (lunation number 221), the new release (陈景润) is out. This release solves a longstanding issue (#228) with the way trajectories were stored, which caused spikes or loops in histories computed at high timewarp. Again, we support three versions of KSP: downloads are available for 1.3.1, 1.3.0 and for 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). See the change log for more details. Thanks to @awang for contributions (fixed a UI bug) during this lunation. 2017-10-19 For the new moon (lunation number 220), the new release (Chasles) is out. A long-standing bug, #1413, initially reported by @maccollo, and also reported by @Cristi, @DaMichel, @goldstarstickergiver, @lyttol, @nanomage, @Parafaragarmus, @rsparkyc, et al., was fixed. This bug prevented landing on peaks of some bodies (notably Minmus) as well as on the Moon in the current version (12) of RealSolarSystem. The fix involves making Principia handle vessels even when KSP's physics operate in a rotating reference frame, all the way down to the ground; as soon as a Kerbal jumps on Minmus, Principia computes its trajectory. Note that vessels within an atmosphere are unaffected; we intend to also handle these down to the ground, but this requires an update in @ferram4's FAR since we want to remain FAR-compatible. Further, Principia now supports KSP 1.3.1; downloads are available for 1.3.1, 1.3.0, and 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). See the change log for details. Thanks to @awang for contributions (clang warning cleanups) during this lunation. 2017-09-20 For the new moon (lunation number 219), the new release (Cesàro) is out. The histories of the vessels are now computed in parallel, speeding up high timewarp on multi-core processors. A bug was fixed that caused a crash when crashing two vessels into each other. Again, we support two versions of KSP: downloads are available for 1.3 and for 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). See the change log for details. 2017-08-21 For the new moon (lunation number 218), which is a total eclipse, the new release (Чебышёв) is out. The speed of the plotting of histories has been improved by about an order of magnitude. The slow plotting in previous versions was responsible for most of the slowdown in map view. Further, the predictions are now plotted smoothly even when they are integrated with a large tolerance. The flight plan now supports burns that guide themselves to follow the Frenet trihedron, e.g., tracking the tangent (prograde), or the binormal (the normal to the orbital plane). Select "Inertially fixed" in the flight planner to use an unguided burn instead, e.g., for spin-stabilized burns. For the first time, Principia supports two versions of KSP: downloads are available for 1.3 and for 1.2.2. Make sure you download the right one (if you don't, the game will crash on load). A couple of bugs reported by @panourgue and @scimas were fixed. See the change log for details. Thanks to @Iskierka and @Jim DiGriz for testing the Linux and Macintosh builds respectively. Note to RSS users: Principia correctly simulates the motion of the moon, so the eclipse occurs as expected when using Principia, even after more than 66 years of numerical integreation, see below. Conversely, without Principia, the Moon's motion cannot be simulated with the requisite accuracy to get correct eclipses, since it is a heavily perturbed orbit. 2017-07-23 For the new moon, the new release (Cayley) is out. It brings trajectories in map view, an update reminder driven by the Moon, a fix to a whole class of off-by-one physics bugs, and further bugfixes. Further, the build includes a binary for Macintosh, thanks to @Jim DiGriz. Note that the version string on Macintosh will mention Cayley-4 instead of Cayley-0. This will be resolved in future versions. See the change log for details. 2017-06-24 For the new moon (lunation number 216), the new release, Cauchy, is out. It brings relative speed markers on nodes, the unification of navball speed mode and reference frame selection, and displaying the trajectory of the target vessel if it moves in the plotting frame. This addresses requests by @lawndart, @maccollo, and @scimas. This release fixes: physics bugs: 1307 reported by @Damien212 and @maccollo, 1404 reported by @Bocian and @lawndart, 1415 reported by @scimas, 1421 reported by @NathanKell and @rsparkyc; a UI bug, 1402, reported by @lawndart and @maccollo; crashes: 1422 reported by @maccollo, 1441 reported by @rsparkyc. See the change log for details. NOTE: due to a forum mishap (stares at @technicalfool ) this thread has changed address, and all followers have been lost; if you had bookmarked the thread or followed it, you may want to do so again. 2017-05-25 For the new moon (lunation number 215), the new release, Catalan, is out. It brings no new features, but fixes a number of bugs and improves the underlying libraries. See the change log for details. 2017-04-26 For the new moon (lunation number 214), the new release, Cartan, is out, bringing with it a utility for rendezvous: the target local vertical local horizontal reference frame. There is a guide to low orbit rendezvous using the new reference frames (screenshots to be added in the near future). See the change log for details. Please read the concepts page carefully, it has been expanded since Cardano. Remember to also have a look at the FAQ if you have a question. Thanks again to @Iskierka for testing the Linux build. 2017-03-28 For the new moon (lunation number 213), the new release, Cardano, is out, bringing with it axial tilt, new reference frames, and timewarp-independent free fall. It marks the beginning of lunar releases. See the change log for details. In particular, note that Cardano is save-incompatible with Cantor. Please read the concepts page carefully, it has been expanded since Cantor. Thanks to @Iskierka for testing the Linux build. 2016-08-13 Cantor is out. This version is mostly the same as بوژگانی (see the change log), the intent is to make sure it is as stable as بوژگانی was: this is the first broadly available release, with a link to binaries outside the IRC channel (see the OP). In the meantime, progress has been ongoing (note that this is about a future release, Cantor contains none of the features below). Regarding our internal libraries, we have clarified the way we handle time (which is always an extremely confusing thing), with our Instant type aligned with Temps Terrestre (TT), and support for date literals in TT, Temps Atomique International (TAI), Coordinated Universal Time (UTC), and UT1 (based on the rotation of the Earth). This allows us to specify dates more cleanly in our tests. We tested the difference between the orbits of Mercury predicted by our ephemeris and by JPL's over a century, and we find the expected error in perihelion precession due to general relativity. On the side of flashier features, we seem to be well underway to having working axial tilt, by tilting universe the current main body (with terrain) is aligned with the axis used by KSP, and rotating the other ScaledSpace models appropriately; in a future release of Principia, the Jupiter, Saturn, and Uranus systems should look much nicer, with the planet properly aligned with its satellites. 2016-06-26 بوژگانی is out. A change log can be found here. 2016-05-20 Burnside is out. A change log can be found here. 2016-05-05 Буняковский is out. A change log can be found here. 2016-02-24 There is a bug in Buffon (2016022220-Buffon-0-g0455d0cb0e4b0b584a84caf40520cf7993903e0c) that causes a crash when starting a new save with RSS (loading an existing save works fine). The hotfix "2016022220-Buffon-12-g1298cffba22d90119bd59e9933a9ef261922a423" (let's call it "Buffon + 12") resolves that, so if you run into this issue just go back to the IRC channel to get the latest build, it will be Buffon + 12. There are no other changes between Buffon and Buffon + 12. 2016-02-22 Buffon is out, you can get it by asking on IRC (#principia on EsperNet), as usual. Changes: The integrators now limit the number of steps they perform, and terminate if their step size vanishes. This avoids issues where the plugin would hang when the trajectory would accidentally get very close to the centre of a celestial body or spend a long time in a low orbit. A use-after-free bug has been fixed which caused a variety of crashes (#872, #881, #889, #896) when the historical trajectory was shortened in a way that would cause it to start after the beginning of the flight plan. The version identifier of the plugin is now displayed in the UI to make it is easier to assert what version is running. A verbosity option has been added to the journalling which makes it easier for us to reproduce crashes. The first two items above are illustrated by the following two reports. For more details see all 19 pull requests between Brouwer and Buffon. 2016-02-11 Some clarifications regarding reference frames and flight planning. 2016-02-09 Brouwer is out, you can get it by asking on IRC (#principia on EsperNet), as usual. User-facing features: The whole Frenet trihedron is now displayed in the correct reference frame when "fix navball in plotting frame" is selected. The initial state (and thus the evolution) of the system is now deterministic even when not using RSS. Tidally locked bodies no longer spin back and forth madly (on the other hand, they may not be tidally locked if their mean period differs from their Jacobi osculating period). When using stock, the Jool system is modified, cancelling the apocalypse. Specifically, we make the inner Jool system nonresonant, since we have been unable to replicate the results (Manley, priv. comm.) according to which some interpretations of the orbital elements yielded a stable Laplace resonance, despite systematic searches of the Jacobi osculating elements. In addition, at Scott Manley (@illectro)'s and @UmbralRaptor's suggestion, we put Bop in a surprisingly stable, though highly precessing, retrograde orbit. The modified system is stable for upwards of a century. Flight planning has been implemented. Modder-facing changes: When a Cartesian initial state cfg is not given, the KSP orbital elements are interpreted in a hierarchical osculating Jacobi fashion; for instance, the orbital elements of Jool are the osculating elements at game start of the orbit of the barycentre of the Jool system around the barycentre of the (sun, moho, eve, gilly, kerbin, mun, minmus, duna, ike, dres) system; the elements of Laythe are the osculating elements at game start of the orbit of Laythe around Jool; the elements of Vall are the osculating elements at game start of the orbit of Vall around the Laythe-Jool barycentre. Optimizations: The Windows build now uses profile-guided optimization (we estimate that this improves performance by ~20%); in theory this could be extended to other platforms. The evaluation of the Чебышёв series has been significantly optimized. @sarbian made trajectory rendering faster (as he pointed out, there is still lots of room for improvement). Other features: Everything that crosses the interface can now be journalled if the right flag is set, allowing us to replay the C++ side of a session; this is useful for tracking down tricky bugs, and it enables profile-guided optimization. Highlights of miscellaneous library changes; beware, this gets technical: In order to get the full Frenet trihedron, which in turn was needed for manœuvres, since the Δv is defined in the Frenet frame at the point of ignition, geometric acceleration (the acceleration of a free-falling trajectory) in any reference frame was needed. To that we created two abstractions, RigidMotion, the derivative of a RigidTransformation, and DynamicFrame, the definition of an arbitrary reference frame. The navigation frames (the frames in which the trajectory is drawn, or with which the manœuvres are defined) implement that (see BodyCentredNonRotatingDynamicFrame and BarycentricRotatingDynamicFrame). In order to interpret the orbital elements of KSP in the hierarchical Jacobi fashion described above, support was added for Kepler orbits (implementation), Jacobi coordinates, and hierarchical systems. Discrete trajectories were reworked, with a heavy dose of CRTP. In preparation for the surface frame in the future, RotatingBody was added. The C++ interface headers and C# extern declarations were repetitive and error-prone, this was exacerbated by the addition of journalling code and replaying code, so a generator was written to produce all of that from an annotated proto. @UmbralRaptor contributed some tests of lunar eclipse timings. For both Kepler orbits and lunar eclipse timings, a simple root finder was needed, bisection does the job for now. A bibliography was written, at @UmbralRaptor's request (it is somewhat out of date). SolarSystem, a class for initializing ephemerides from protobuf text format configuration files for testing purposes was written. A script for generating the initial state configuration files from the emails sent by JPL's HORIZONS system was written (the gravity model configuration file is hand-curated). An utility turns the protobuf text format configuration files into KSP ModuleManager configuration files for RSS support. Various geometric utilities were added: angles (implementation), spherical coordinates (more are needed). More C++11/14 features were used as they became available (for instance, the units are now constexpr), in addition we now use std::experimental::optional. C++14-related improvements were made to not_null. For more details, see all 195 pull requests between Bourbaki and Brouwer. 2015-08-16 Bourbaki is out, you can get it by asking on IRC (#principia on EsperNet), as usual. Please bear in mind that the channel operators may be away from keyboard, so you should wait until you're noticed (it also helps to say the name of the channel operators since that pings them). As of 2015-08-16T15:38Z, the build for Win32 is ready, we're waiting for Norgg and armed_troop for the Linux and Macintosh builds respectively. Note that you should read the FAQ before installing principia. Rough changelog: Reimplemented integrators: the symplectic Runge-Kutta-Nyström integrator was reimplemented more cleanly, an embedded explicit Runge-Kutta-Nyström integrator was implemented. Abstractions for differential equations were created. Ephemeris: the celestial bodies are integrated on their own, with their own (much larger) timestep (45 min); their trajectories are then fitted using чебышёв series, yielding continuous trajectories. This means that when there are no vessels (including asteroids, see the FAQ), timewarp at very high speed (6'000'000x was tested in RSS) is smooth. The predictions are computed using an adaptive step size, so they're faster and less fiddly (you still get a tolerance setting, but it doesn't need as much attention as the step size setting; the step size will shorten near periapsis and lengthen near apoapsis on its own). The histories are still in fixed steps of 10 s, that will likely change in Brouwer, since it is one of the biggest performance costs now. There is an initial configuration for Real Solar System: the planets will start in the right places as given by the JPL HORIZONS service, and they are given gravity models using the freshest data available (Vesta's model is from Dawn data, some Cassini data gets used). Please note the RSS-specific recommendations in the FAQ. A side effect of that is that the moon becomes far more accurate: since the motion of the moon is very much a 3-body problem, it cannot be accurately represented in RSS alone. In particular, real-life eclipses can be observed in principia + RSS (please note the unexpected inaccuracy mentioned in the FAQ). This initial configuration also includes J2 for the Sun, the planets, the Moon, and Vesta, so the resulting effects are felt (precession of Earth orbits, the possibility of heliosynchronous orbits, etc.). Bourbaki is save-compatible with Borel, for RSS users, please note that unless you reset the plugin, the new initial state and gravity model configuration files will not be taken into account. 2015-05-07 The new version, Borel, is out (you can get it on IRC, as previously; the same caveats apply). Rough changelog: ported to 1.0.x (that only took a couple of lines); custom navball settings, so that the navball can be fixed in the reference frame in which the trajectory is plotted; the IVA navball is unaffected; when using the custom navball, the prograde/retrograde vectors are now in the correct reference frame, consistent with what is shown is map view; the rest of the Frenet trihedron (the radial and normal vectors) are unaffected at the moment and will be fixed in another version; fixed a few bugs (the tetrydsbug, the melonbug, the thutmosebug); less memory-hungry; added a setting to clip histories; added a toolbar button to show/hide the UI; the UI now acknowledges the F2 key; other things that I forgot. Moreover, Norgg and armed_troop have made good progress on Linux 64-bit and Macintosh 32-bit builds respectively, so if you're on these platforms you can go on IRC and ask for a build or for build instructions. With Windows 32-bit, Linux 64-bit and Macintosh 32-bit, we should be covering most users (I don't think it's worth doing a Linux 32-bit build). 2015-03-22 Serialization has been implemented, and rudimentary predictions have been added. The predictions are currently using the same integration method (McLachlan and Atela's 1992 optimal 5th order method), with the same splitting of the Hamiltonian (kinetic + potential energy), this is somewhat usable but unacceptably slow. I am currently implementing as many symplectic integrators as I can find in order to compare them, and I will also be comparing various splittings (as as nonsymplectic methods in use for computing ephemerides). I will probably write a post about these at some point (probably an advanced one, rather than an elementary introduction, this is quite a complicated topic). It seems that there is some interest in builds of Principia, no matter how unstable or slow they may be. If you want to try out the current version of Principia (Bolzano) for the Windows 32-bit version of KSP, go the IRC channel linked below and ask me for a build (my nickname there is egg, or sometimes something of the form egg|<status>|egg). CAVEAT: The current version is not stable, it can corrupt or otherwise destroy saves, it has been known to crash, and predictions are horrendously slow. #principia IRC channel on EsperNet. 2015-01-22 The refactoring of the physics bubble has been done (and some tests have been added), as well as some cleanup in the C# adapter (including some performance improvements, a lot of the performance issues occur on the C# side since the implementation is a bit careless there). More refactoring occurred (use of a not_null template for non-null pointers). The next step on the path towards playability is persistence: the state of the plugin must be persisted so that we remember the states of the planets, the histories of the vessel trajectories, etc. (currently loading a save or reverting will result in either a crash or a loss of consistency due to the planets having moved around). Persistence of our types will be achieved using protocol buffers, stored in config nodes: we don't want to use KSP's config format directly, since we have lots of highly structured data and operate far from KSP's API it would be inefficient and clumsy. We'll probably also use protobufs for caching when implementing trajectory predictions later on. Some work has already been done in that direction. Here are some more screenshots, showing a flight from Kerbin to the Kerbin-Mun L4 Lagrange point (the reference frame for each screenshot is indicated in the "Traces of various description" window). antedated 2014-12-13 Support for intrinsic acceleration has been added. Refactoring will be needed, but it works, as demonstrated by the following plane change manÅ“uvre: 2014-11-07 Some work has been done on better abstractions for rendered trajectories, nothing significant yet (in particular there still is something in Õ(n) which could be in Õ(1), runs at each frame, where the constant factor involves evaluating trig functions, and n~10_000 is the number of rendered points, so that rendering trajectories in the barycentric rotating frame is slow), but some pretty pictures. This shows a vessel near the L5 point of the Kerbin-Mun system. In the first image, the trajectory of the vessel is displayed in the nonrotating reference frame centred on the Mun, in the second it is displayed in the nonrotating reference frame centred on Kerbin, and in all subsequent images it is displayed in the barycentric corotating reference frame of the Kerbin-Mun system. Work on intrinsic acceleration is ongoing. 2014-10-28 Code has been written to plot the trajectories in nonrotating body-centred reference frames (and barycentric corotating, not reviewed yet). While abstractions will have to be written to do that more cleanly and efficiently, this yields some pretty pictures. Caveat lector: While some of the following orbits may look very wild, bear in mind they are in non-inertial reference frames. Two of these wilder trajectories are followed by the same trajectory in a more pedestrian reference frame. In the Kerbin-centric non-rotating reference frame, they would all look like two or three elliptic orbits connected by strange segments where the perturbation by the Mun is to blame. The last picture below (in the barycentric corotating frame of the Kerbin-Mun system, that is, the unique frame in which the Kerbin-Mun barycentre as well as the line through Kerbin and the Mun are invariant) shows a trajectory that differs strongly from what stock KSP would have yielded: in stock this would have been a circular orbit around the Mun near the edge of its SoI. Instead it is a transfer to an eccentric Kerbin orbit, which is picked up by the Mun again after a while and ends with a crash on the Mun. With the addition of plotting, the C++ plugin has caught up with the features of the initial C# prototype. After the abstractions for plotting are written (we will add the remaining interesting reference frames in the process), the next step will be to take care of altering the trajectory when, e.g., engines are used. It is apparent that the C++ plugin is significantly faster, much more reliable, and easier to debug than the C# prototype (it is also correct; some hasty shortcuts were made in the prototype that resulted in unreliable initial states and other problems). 2014-09-30 Trajectory, an abstraction for a tree of trajectories that can be forked into child alternatives (useful i.e. for predictions, manoeuvre nodes, but also simply computations at different precisions), has been written (part of the physics namespace) The plugin has returned, first as a simple orbit-freezing plugin, then as a plugin that actually integrates the motion of vessels (only on-rails for the moment). Is does not plot yet, so it is still behind the C# prototype in terms of features, but it is significantly faster. As was previously mentioned, all calculations are done in a native assembly, called by P/Invoke via a (cdecl) interface. It should be noted that the plugin uses glog everywhere for logging (since logging from native code is needed). Of course, this means Principia will have its own log files (in <KSP directory>/glog/Principia, with a log of the last session in <KSP directory>/stderr.log. Another interesting aspect is that there will be no silent exceptions as in managed plugins, instead, the game will either segfault (when dereferencing an invalid pointer) or abort (SIGABRT) if a glog CHECK macro fails (on Windows the latter yields the "KSP.exe has stopped working" message). I have been informed by Sarbian et alii that this will result in Fun support. 2014-07-04 I wrote the second explanatory post, on Hamiltonian mechanics (PDF). Prerequisites are chapters 4, 8, and sections 11-4 and 11-5 of Richard Feynman's Lectures on Physics. The next post will be on symplecticity and the leapfrog integrator. 2014-06-27 The integrator (still a 5th order SPRK, same as in the C# prototype, the Saha & Tremaine stuff isn't here yet) has been implemented, tested and benchmarked (using a Windows port of google/benchmark) in C++, as well as the first level of abstraction above it, principia::physics::NBodySystem (header, body, test, header for test data, test data, test of test data (which is also a nice example of the use of principia::quantities and principia::geometry, benchmark (using the test data)). A significant change of plans has occured: As Unity uses the .NET Framework v2.0, it is not possible to use plugins compiled for the Framework v4.5. This means C++/CLI projects need to be compiled using the platform toolset v90 (from VS2008), rather than VS2013's v120. Of course v90 does not support C++11 nor C++14, so it is not an option for this code that strongly depends on C++11 features. As a result, we will keep using the C++11 codebase, compiling it to a native DLL, and using P/Invoke to call it from a C# adapter. The C# adapter will perform no calculations, only transmit data from KSP to the native plugin and apply the changes/render the trajectories returned by the plugin. A simple test P/Invoke plugin can be seen on the repository (header, body, C# adapter) and works in KSP. This means there will be separate x86 and AMD64 builds for each target operating system (Microsoft Windows and 57 varieties of Unix), possibly more if we decide to do specific optimisations for Intel chips (though ICC is not cheap). Moreover, this will allow a switch to clang in the near future, so that we can have saner error messages and better compliance with the standard. 2014-05-12 I now have a collaborator on Principia, https://github.com/pleroy (my father). This means the code gets reviewed and that development is faster. We have decided to completely switch to C++/CLI due to better test tools and useful language features. Most of the code will actually be written in standard C++, with the implementation inlined in header files, so that they are seen by the eventual C++/CLI managed assembly (If we were to use C++/CLI everywhere, we would need managed boundaries between the assemblies, which is quite inconvenient). As an added advantage, using standard C++ enables putting performance-critical parts into a native assembly if needed at a later time, without requiring a significant rework of the code. We have started switching to gmock, gtest and glog for mocking, testing and logging. These tools are more convenient and powerful than the Visual Studio testing framework and are open source, so that users of Visual Studio Express (which does not support Microsoft's testing framework) will be able to build and run tests if they want to. Here is the first test to be converted to gtest: https://github.com/mockingbirdnest/Principia/blob/master/geometry/sign_test.cpp. 2014-04-03 The Quantities library (C++) is pretty much done and tested. I am currently porting the C# Geometry assembly mentioned previously (now called CTSGeometry) to C++ in order to enable its use with these quantities. 2014-03-15 The Geometry assembly seems to be mostly feature complete, so I'll start writing tests tomorrow (Saturday) after changing a few access modifiers, replacing the ugly switch statements in Permutation by something nicer, and a few optimisations. See here for an overview of its features. 2014-03-04 I have investigated the feasibility of using other languages for KSP plugins: The following languages can be used on their own to write a plugin: C#(unsurprisingly), F#, C++/CLI (with no calls to native code). VB.NET can be used, but wrappers in one of the above languages are needed due to its case-insensitivity. Unity does not support mixed-mode DLLs, so calls to native code have to be made using DllImports in one of the above languages. I have started doing some refactoring since the sphaghettiness of the code was getting on my nerves. I have written strongly typed wrappers for the numerous reference frames spawned by KSP (direct vs. indirect, rotating vs. inertial, world vs. body-centric, etc.) as I have had numerous bugs due to a misplaced xzy, rotation, translation, scaling, inertial force etc. Of course, since KSP has the brilliant idea of using both direct and indirect reference frames, I needed distinct types for vectors, bivectors and trivectors (basically I had to strongly type Grassmann algebras; there can be no cross product, only wedge products, commutators and left and right actions of alternating forms---where is identified with through the inner product, and is identified with ). I do not think I will implement strong typing for physical quantities yet (though I'd like to), since C# generics are not powerful enough for that; I would need C++ templates. I'll do that when I rewrite things in C++/CLI. The next step is to implement my own versor, since Unity's Quaternion is in single-precision float and KSP's QuaternionD is broken. The rest should be more straightforward refactoring. 2014-02-24 It turns out I have trouble properly setting the position when off-rails (finding out where the reference frame actually is is hard). However, there are some nicer news: I seem to have found the source of the phantom acceleration bias (not the ones arising from rotation, the bias that is removed by timewarping). The floating origin sometimes floats several km away from the ship, so that's probably just floating-point inaccuracies (the usual Kraken). If that hypothesis turns out to be true, this particular acceleration bias will be easy to fix, just reset the floating origin often enough. 2014-02-19 I have successfully implemented the integration of proper acceleration for the active vessel when off-rails. Further experimentation on proper acceleration has led me to the following conclusions: There is a bias in proper acceleration coming from some improperly initialised variable in KSP. Indeed, when loading a vessel in LKO, I observe a strong bias in proper acceleration (~20 mm s-2). This bias is observed independently of the way proper acceleration is computed (differentiating position twice, differentiating any of the numerous velocities, etc.) and geometric accelerations have been checked from first principles (the difference in geometric acceleration depending on the point of the vessel it is computed at is negligible). The bias is reduced to below 1 mm s-2 when warping then coming out of warp. It should be noted that the strong bias is not seen in Vessel.perturbation, but Vessel.perturbation consistently has a bias of 4 mm s-2. As I have attempted to compute the proper acceleration in many different ways and all were consistent with each other and inconsistent with Vessel.perturbation, I assume Vessel.perturbation is mostly nonsense. Accelerations below 1 mm s-2 are biased, unavoidable, unusable in stock, and should be clamped to 0. The acceleration from low-thrust engines will have to be fetched by hand. It had previously been mentioned that spinning the ship accelerates it. If spinning the ship with angular velocity É produces a phantom acceleration a, then spinning it with angular velocity -É produces a phantom acceleration -a. It seems a is either prograde or retrograde. 2014-02-17 I have finally managed to work on this a bit over the weekend. Extensive experimentation has failed to yield a better velocity, so we are stuck with computing the proper acceleration from the rather mysterious Vessel.obt_velocity for now (for some reason in whatever reference frame this velocity is in, the geometric accelerations are as expected, except for the Coriolis acceleration which is halved ). This yields roughly the same results as Vessel.perturbation without the moving average. The same experiments have further shown that a naïve low-pass filter will not be enough to remove Unity's silliness. For instance, one finds the proper acceleration is strongly correlated with the rotation rate of the ship. Smarter post-processing will be needed. I shall now attempt to actually integrate whatever proper acceleration I have managed to grab. I also wrote the first explanatory post, which describes ODEs and Runge-Kutta methods (PDF). I have tried not only to explain how Runge-Kutta methods work (this can easily be found on Wikipedia) but why they have this structure. Hopefully you will find it interesting. 2014-02-08 I fixed a bug or two since 2014-02-05, added a few TODOs, but have not cleaned up the code to any measurable extent. I am, however, publishing it on GitHub (under the MIT license). Caveat Compilator: As previously stated, this is just a proof of concept with a bunch of traces. Pressing the wrong buttons in the wrong order will result in lots of NullReferenceExceptions and off-rails crafts will behave weirdly. Using HyperEdit to set up initial conditions, then switching to Newtonian physics and fooling around with reference frames can be entertaining though. You might learn something from looking at the Integrators part (which admittedly contains only one integrator), the rest was quickly hacked together, has no tests, is badly structured &c. The 'Simulator' project probably won't compile, it's leftover from my Alternis Kerbol simulations. It's not needed. 2014-02-05 This is currently hardly more than a proof of concept. The simulation only affects on-rails vessels, thrust is ignored (thus you can't actually play while the simulation is running) and the integrator is too slow. However, it shows a few interesting things: Near-unit-roundoff (using IEEE 754 binary64) errors can be achieved while sustaining 100_000x timewarp with B = 17, V < 5. Handwavy asymptotic calculations indicate that for V = 100, this integrator would slow down to about 20_000x timewarp. Using better integrators (and saner tolerances), performance could easily be increased by a couple of orders of magnitude, making the simulation usable for RSS as well as stock. Trajectory plotting in rotating reference frames, or reference frames centered around a body other than the primary, can be useful even for near-Keplerian orbits: it allows for visualisation of RT2 satellite coverage, easier landing prediction, etc. The stock integrator is terrible, and will have to be overriden at all times while in space (when near a Lagrange point, a fraction of a second under stock integration will turn a Kerbin capture into a Mun collision). If you think floating SOIs (or worse yet, SOIs with repulsive gravity) are a half-decent model for Lagrange points, you don't really understand how Lagrange points work. Expect a slow development cycle, due to a combination of laziness, exams, and this actually being a complicated project. I'll put the source on GitHub as soon as I can clean things up a bit (there are quite a few traces that were too hastily implemented for my taste). This might take a few days, see above. Nonetheless, here are some pictures that illustrate the fun trajectories in the N-body problem. The second and third pictures have a misplaced trajectory, this bug has been fixed. Some pictures have three strange red, green and blue lines, which indicate the origin and axes of world space. Notations Terminology Considerations on numerical integration The current prototype uses a straightforward fifth order SPRK method. The coefficients used are from (Atela & McLachlan 1992). The increments are accumulated using Kahan summation. The integration is performed with a constant 10 second timestep (numerical experiments suggest that the error is close to an unit roundoff with a 5 second timestep for LKO). Regarding implementation details, the integrator is written in C# (compiled with VS2013) and uses double (IEEE 754 binary64) for all computations. Scott Manley suggested using hybrid symplectic integrators (Chambers 1999) in order to speed things up. It should be noted that the concerns that the Chambers paper attempt to alleviate might not be critical for gameplay purposes (the main integration can probably be done with a very small timestep compared to the ones commonly used in astronomy. Moreover, timestep reduction occurs de facto when getting out of warp, as the game cannot conceivably be played with timesteps of several seconds). It could become relevant for trajectory predictions in vessels under thrust, which has to be done in a few hundred milliseconds over several years. For those predictions, the timestep would have to be increased to durations comparable to those used in the paper, and similar concerns would arise. The results from the papers quoted by Chambers, namely (Saha & Tremaine 1994) and (Holman & Wisdom 1991), will probably have to be used in order to make the main integrator faster. Experiments will have to be carried out in order to find out whether a higher order (> 2) integrator is worth using, and how the added cost of Keplerian evolution (which requires numerically solving the Kepler equation for all bodies, which is very costly due to the trigonometric functions) affects performance at acceptable time steps. Open questions for the interested reader Regarding KSP modding The method I currently use for drawing trajectories (LineRenderers, object in layer 9, transform.parent = null, useWorldSpace=true, updated every time the GUI is drawn) has some issues: when rotating the camera in map mode, the lines lag behind. Does this have a known solution? (I guess so, RT2 doesn't have this problem). And indeed, the RT2 code contained the solution. Thanks, Cilph! Is there a way to directly set the position and velocity of the planets and vessels in world coordinates? OBE, the API does not make sense in highly original ways. Can anybody think of a way to mod in axial tilt (even a hacky one; remember that I'm the one moving the planets around anyway)? OBE (done in RSS, we actually have axial tilt, it's just that all planets rotate around parallel axes). Regarding aerodynamics Could somebody help me with the implementation of orbital decay drag when I get to implementing that? ferram4 told me he'd help. Thanks! Would it be conceivable to predict the results of aerobraking/aerocapture/ballistic reentry with FAR (within some error margins, to be displayed on the predicted trajectory)? How slow would that be? Answered by ferram4. This might end up happening. Regarding astrophysics and astrodynamics The uniformly rotating reference frame around the barycenter with respect to which the two massive bodies are fixed is very useful when looking at trajectories in the CR3BP (Lagrange 1772). What would a good reference frame for the ER3BP (for bodies with highly eccentric orbits, e.g., Eeloo in stock, Pluto in RSS) be? the uniformly rotating one around the barycenter that follows the mean anomalies, the nonuniformly rotating one that follows the true anomalies, or something else entirely? In the rotating-pulsating reference frame that fixes both bodies, the equilibrium points are fixed. Is there a way to draw things in that reference frame on the in-game map that's not too confusing? Can it still be useful to draw the potential for the parts of the equations of motion that derive from a potential, given that the independent variable is true anomaly rather than time? Should long-term trajectory predictions for vessels under thrust be inaccurate, is there a good way of estimating the uncertainty (for instance, would predicting a few perturbed trajectories and plotting them all give a representative idea of what might happen)? ferram4 suggested a few interesting things. Would drawing the gravitational potential in the current orbital plane (together with the centrifugal potential if orbits are drawn is a rotating reference frame) be useful? Answered by ferram4 with visualisation suggestions. The answer is 'yes'. How should stationkeeping be implemented? In particular, how should the user set the orbit they want to maintain? Regarding the KSP fora Do we have LATEX support? If that isn't the case, is it conceivable to have it in the foreseeable future? Further modding Once the mod gets to a functional state (taking thrust into account), I shall attempt to solve the problem of trajectory prediction for vessels under thrust. In the process, the smarter integrators mentioned above will be implemented, and the most efficient one will be kept. This should significantly increase computation speed. This will also enable instantaneous-burn maneuver nodes (the kind of maneuver node we have now). The barycenters will be fixed in order to stabilise the Jool system. Scott Manley (illectro)'s predictions indicate this will make it stable over at least 1_000 years (Pol was not part of those predictions, its stability remains to be determined). Speed will be further increased by rewriting the numerical integration in (unmanaged) C++, interfaced with C# through C++/CLI. The unmanaged C++ (compiled with clang) will use 80-bit extended precision 'long double' (64-bit mantissa instead of 53-bit) for added precision. Once the mod becomes playable with N-body gravitation with point masses, the following effects should be relatively easy to add: Conservation of angular momentum through timewarp and outside timewarp (allowing for spin-stabilisation and thus fixed RT2 antennae if Cilph decides to implement that); Thrust through timewarp, for ion engines and the like, together with maneuver nodes for non-instantaneous burns; Orbital decay drag, with ferram4's help; Stationkeeping, to deal with orbital decay and unstable weakly bound orbits; Gravitational moment (quadrupole) for planets, enabling such amusing things as Sun-synchronous orbits; Insert crazy idea here... Acknowledgements I would like to thank (in alphabetical order of forum usernames) Anatid for his attempt at documenting the KSP API, armed_troop for his help in making the codebase clang-compatible. Ezriilc, Forecaster, khyperia, Payo and sirkut for their HyperEdit plugin, which is really useful for setting up initial conditions, Scott Manley (illectro) for his help with numerical integration of the N-body problem, Matt Roesle (Mattasmack) for writing an integrator which was far better than the one I used, thus prompting me to write my current SPRK integrator, NovaSilisko for his Alternis Kerbol mod, which piqued my interest in the simulation of the N-body problem, The entire KSP modding community (especially the subset which writes clean, well-commented code) for providing code examples from which one can learn the subtleties of dealing with the KSP API. If I forgot you in the above list, please complain! Bibliography Mathematica documentation on SPRK methods. [Atela & McLachlan 1992] Robert I McLachlan and Pau Atela, The accuracy of symplectic integrators, 1992. [Chambers 1999] John E. Chambers, A hybrid symplectic integrator that permits close encounters between massive bodies, 1999. [Holman & Wisdom 1991] Jack Wisdom and Matthew Holman, Symplectic maps for the N-body problem, 1991. [Kenniston 2002] Michael Kenniston, Dimension Checking of Physical Quantities, 2002. [Lagrange 1772] Joseph-Louis Lagrange, Essai sur le problème des trois corps, 1772. [saha & Tremaine 1994] Prasenjit Saha and Scott Tremaine, Long-term planetary integration with individual time steps, 1994. [Tao 2012] Terence Tao, A mathematical formalisation of dimensional analysis, 2012. Eric Weisstein's World of Physics, Gravitational Moment. [Yoshida 1990] Haruo Yoshida, Construction of higher order symplectic integrators, 1990. [Yoshida 1992] Haruo Yoshida, Symplectic Integrators for Hamiltonian Systems: Basic Theory, 1992.

Hi. I found this amazing mod that generates n-body orbital mechanics known as Principia, by @eggrobin. Even the planets work with the new mechanics, knocking each other's orbits around in a quite interesting fashion, the same way it's done in real life. It even reworks the Jool system to make sure the moons don't go completely out of whack. The problem is, it only seems to work with stock KSP. There are many planet packs out there which do not get reworked for compatibility with this mod. What I am doing with Planet Patches is adding a patch for each planet mod I come across that has unstable orbits with Principia, repositioning the unstable bodies to make them stable. Modified Planet Packs: Planned Planet Packs: I am open to requests. In fact, I plan on building this entire thing on requests Requests I will not take: Half-baked mods - what I mean here is, mods that are so in-development that they can't even work properly on their own. For example, if the SOIs are insanely sized in a way that completely messes up one's ability to travel. Kopernicus mods from before KSP 1.2.2 - sorry, but the earliest KSP version for Principia is 1.2.2, and I really can't go back further than that, unless the mod does work on 1.2.2 or above. Other than that, I hope to take every single request that I can! Download - Github

This thread is devoted to people who want to build Principia themselves, either for security reasons, because they want to build from the latest commit, or because they use a platform other than Windows, Ubuntu, or MacOS. Please post your questions/concerns/flames here and do not pollute the main Principia thread. ― The Principia co-authors, @pleroy and @eggrobin.