From 89196a32c3a52ddc853accb1c648cf27f49b8c4f Mon Sep 17 00:00:00 2001
From: Lamont Granquist <lamont@scriptkiddie.org>
Date: Tue, 22 Aug 2023 15:37:26 -0700
Subject: [PATCH] ChangeOrbitalElements now uses Forward AutoDiff via Dual
 numbers/vectors

Signed-off-by: Lamont Granquist <lamont@scriptkiddie.org>
---
 MechJeb2/MechJeb2.csproj                      | 482 +++++++++---------
 MechJeb2/MechJebLib/Core/Maths.cs             |  43 +-
 .../Maneuvers/ChangeOrbitalElement.cs         |  89 +++-
 MechJeb2/MechJebLib/Primitives/Dual.cs        |  67 +++
 MechJeb2/MechJebLib/Primitives/DualV3.cs      |  62 +++
 MechJebLibTest/Maths/FunctionsTests.cs        |   8 +-
 6 files changed, 486 insertions(+), 265 deletions(-)
 create mode 100644 MechJeb2/MechJebLib/Primitives/Dual.cs
 create mode 100644 MechJeb2/MechJebLib/Primitives/DualV3.cs

diff --git a/MechJeb2/MechJeb2.csproj b/MechJeb2/MechJeb2.csproj
index 10c0b887..e26c1341 100644
--- a/MechJeb2/MechJeb2.csproj
+++ b/MechJeb2/MechJeb2.csproj
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="utf-8"?>
 <Project ToolsVersion="12.0" DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
-    <Import Project="$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props" Condition="Exists('$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props')" />
+    <Import Project="$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props" Condition="Exists('$(MSBuildExtensionsPath)\$(MSBuildToolsVersion)\Microsoft.Common.props')"/>
     <PropertyGroup>
         <Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
         <Platform Condition=" '$(Platform)' == '' ">AnyCPU</Platform>
@@ -12,7 +12,7 @@
         <TargetFrameworkVersion>v4.8</TargetFrameworkVersion>
         <NoStdLib>true</NoStdLib>
         <FileAlignment>512</FileAlignment>
-        <TargetFrameworkProfile />
+        <TargetFrameworkProfile/>
         <NuGetPackageImportStamp>
         </NuGetPackageImportStamp>
         <LangVersion>8</LangVersion>
@@ -40,245 +40,247 @@
         <CodeAnalysisRuleSet>MechJeb2.ruleset</CodeAnalysisRuleSet>
     </PropertyGroup>
     <ItemGroup>
-        <Compile Include="AttitudeControllers\BaseAttitudeController.cs" />
-        <Compile Include="AttitudeControllers\BetterController.cs" />
-        <Compile Include="AttitudeControllers\HybridController.cs" />
-        <Compile Include="AttitudeControllers\KosAttitudeController.cs" />
-        <Compile Include="AttitudeControllers\MJAttitudeController.cs" />
-        <Compile Include="AttitudeControllers\KosPIDLoop.cs" />
-        <Compile Include="AttitudeControllers\TorquePI.cs" />
-        <Compile Include="AutopilotModule.cs" />
-        <Compile Include="CachedLocalizer.cs" />
-        <Compile Include="CelestialBodyExtensions.cs" />
-        <Compile Include="CompatibilityChecker.cs" />
-        <Compile Include="ComputerModule.cs" />
-        <Compile Include="DisplayModule.cs" />
-        <Compile Include="FlyingSim\SimulatedParachute.cs" />
-        <Compile Include="FlyingSim\SimulatedPart.cs" />
-        <Compile Include="FlyingSim\SimulatedVessel.cs" />
-        <Compile Include="FuelFlowSimulation.cs" />
-        <Compile Include="FuelNode.cs" />
-        <Compile Include="FuelStats.cs" />
-        <Compile Include="GlobalSuppressions.cs" />
-        <Compile Include="GLUtils.cs" />
-        <Compile Include="GuiUtils.cs" />
-        <Compile Include="InstallChecker.cs" />
-        <Compile Include="LandingAutopilot\CoastToDeceleration.cs" />
-        <Compile Include="LandingAutopilot\CourseCorrection.cs" />
-        <Compile Include="LandingAutopilot\DecelerationBurn.cs" />
-        <Compile Include="LandingAutopilot\DeorbitBurn.cs" />
-        <Compile Include="LandingAutopilot\FinalDescent.cs" />
-        <Compile Include="LandingAutopilot\KillHorizontalVelocity.cs" />
-        <Compile Include="LandingAutopilot\LowDeorbitBurn.cs" />
-        <Compile Include="LandingAutopilot\PlaneChange.cs" />
-        <Compile Include="LandingAutopilot\UntargetedDeorbit.cs" />
-        <Compile Include="Maneuver\Operation.cs" />
-        <Compile Include="Maneuver\OperationAdvancedTransfer.cs" />
-        <Compile Include="Maneuver\OperationApoapsis.cs" />
-        <Compile Include="Maneuver\OperationCircularize.cs" />
-        <Compile Include="Maneuver\OperationCourseCorrection.cs" />
-        <Compile Include="Maneuver\OperationEccentricity.cs" />
-        <Compile Include="Maneuver\OperationEllipticize.cs" />
-        <Compile Include="Maneuver\OperationInclination.cs" />
-        <Compile Include="Maneuver\OperationInterplanetaryTransfer.cs" />
-        <Compile Include="Maneuver\OperationKillRelVel.cs" />
-        <Compile Include="Maneuver\OperationLambert.cs" />
-        <Compile Include="Maneuver\OperationLan.cs" />
-        <Compile Include="Maneuver\OperationLongitude.cs" />
-        <Compile Include="Maneuver\OperationMoonReturn.cs" />
-        <Compile Include="Maneuver\OperationPeriapsis.cs" />
-        <Compile Include="Maneuver\OperationPlane.cs" />
-        <Compile Include="Maneuver\OperationResonantOrbit.cs" />
-        <Compile Include="Maneuver\OperationSemiMajor.cs" />
-        <Compile Include="Maneuver\OperationTransfer.cs" />
-        <Compile Include="Maneuver\PlotArea.cs" />
-        <Compile Include="Maneuver\Porkchop.cs" />
-        <Compile Include="Maneuver\TimeSelector.cs" />
-        <Compile Include="Maneuver\TransferCalculator.cs" />
-        <Compile Include="MathExtensions.cs" />
-        <Compile Include="MechJebAR202.cs" />
-        <Compile Include="MechJebCore.cs" />
-        <Compile Include="MechJebLib\Control\PIDLoop.cs" />
-        <Compile Include="MechJebLib\Core\Bisection.cs" />
-        <Compile Include="MechJebLib\Core\BrentMin.cs" />
-        <Compile Include="MechJebLib\Core\BrentRoot.cs" />
-        <Compile Include="MechJebLib\Core\FunctionImpls\RealDeltaVToChangeApoapsisPrograde.cs" />
-        <Compile Include="MechJebLib\Core\FunctionImpls\RealSingleImpulseHyperbolicBurn.cs" />
-        <Compile Include="MechJebLib\Core\Functions\Interpolants.cs" />
-        <Compile Include="MechJebLib\Core\Functions\Maneuvers.cs" />
-        <Compile Include="MechJebLib\Core\Maths.cs" />
-        <Compile Include="MechJebLib\Core\Functions\Angles.cs" />
-        <Compile Include="MechJebLib\Core\Gooding.cs" />
-        <Compile Include="MechJebLib\Core\ODE\BS3.cs" />
-        <Compile Include="MechJebLib\Core\ODE\DP5.cs" />
-        <Compile Include="MechJebLib\Core\ODE\AbstractIVP.cs" />
-        <Compile Include="MechJebLib\Core\ODE\AbstractRungeKutta.cs" />
-        <Compile Include="MechJebLib\Core\ODE\Event.cs" />
-        <Compile Include="MechJebLib\Core\TwoBody\Shepperd.cs" />
-        <Compile Include="MechJebLib\Core\TwoBody\Farnocchia.cs" />
-        <Compile Include="MechJebLib\Maneuvers\ChangeOrbitalElement.cs" />
-        <Compile Include="MechJebLib\Maneuvers\ReturnFromMoon.cs" />
-        <Compile Include="MechJebLib\Primitives\Vn.cs" />
-        <Compile Include="MechJebLib\Primitives\Scale.cs" />
-        <Compile Include="MechJebLib\PVG\ContinuityLayout.cs" />
-        <Compile Include="MechJebLib\PVG\InputLayout.cs" />
-        <Compile Include="MechJebLib\PVG\OutputLayout.cs" />
-        <Compile Include="MechJebLib\PVG\AscentBuilder.cs" />
-        <Compile Include="MechJebLib\PVG\Integrators\IPVGIntegrator.cs" />
-        <Compile Include="MechJebLib\PVG\Integrators\VacuumCoastAnalytic.cs" />
-        <Compile Include="MechJebLib\PVG\Integrators\VacuumThrustAnalytic.cs" />
-        <Compile Include="MechJebLib\PVG\Integrators\VacuumThrustIntegrator.cs" />
-        <Compile Include="MechJebLib\PVG\Ascent.cs" />
-        <Compile Include="MechJebLib\PVG\Phase.cs" />
-        <Compile Include="MechJebLib\PVG\Problem.cs" />
-        <Compile Include="MechJebLib\PVG\OptimizerBuilder.cs" />
-        <Compile Include="MechJebLib\PVG\ResidualLayout.cs" />
-        <Compile Include="MechJebLib\PVG\Solution.cs" />
-        <Compile Include="MechJebLib\PVG\Optimizer.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle3Energy.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle4Energy.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle4Reduced.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle4Propellant.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle5Reduced.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\Intercept6Cartesian.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\IPVGTerminal.cs" />
-        <Compile Include="MechJebLib\Primitives\H1.cs" />
-        <Compile Include="MechJebLib\Primitives\H3.cs" />
-        <Compile Include="MechJebLib\Primitives\HBase.cs" />
-        <Compile Include="MechJebLib\Primitives\Hn.cs" />
-        <Compile Include="MechJebLib\Primitives\M3.cs" />
-        <Compile Include="MechJebLib\Primitives\Q3.cs" />
-        <Compile Include="MechJebLib\Primitives\V3.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\Kepler3Reduced.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\Kepler4Reduced.cs" />
-        <Compile Include="MechJebLib\PVG\Terminal\Kepler5Reduced.cs" />
-        <Compile Include="MechJebLib\Simulations\SimVesselManager.cs" />
-        <Compile Include="MechJebLib\Simulations\SimVesselUpdater.cs" />
-        <Compile Include="MechJebLib\Suicide.cs" />
-        <Compile Include="MechJebLib\SuicideBuilder.cs" />
-        <Compile Include="MechJebLib\Utils\BackgroundJob.cs" />
-        <Compile Include="MechJebLib\Simulations\SimVesselBuilder.cs" />
-        <Compile Include="MechJebLib\Simulations\DecouplingAnalyzer.cs" />
-        <Compile Include="MechJebLib\Simulations\FuelFlowSimulation.cs" />
-        <Compile Include="MechJebLib\Simulations\FuelStats.cs" />
-        <Compile Include="MechJebLib\Simulations\PartModules\SimModuleRCS.cs" />
-        <Compile Include="MechJebLib\Simulations\SimPart.cs" />
-        <Compile Include="MechJebLib\Simulations\SimPartModule.cs" />
-        <Compile Include="MechJebLib\Simulations\PartModules\SimLaunchClamp.cs" />
-        <Compile Include="MechJebLib\Simulations\PartModules\SimModuleDecouple.cs" />
-        <Compile Include="MechJebLib\Simulations\PartModules\SimModuleDockingNode.cs" />
-        <Compile Include="MechJebLib\Simulations\PartModules\SimModuleEngines.cs" />
-        <Compile Include="MechJebLib\Simulations\PartModules\SimProceduralFairingDecoupler.cs" />
-        <Compile Include="MechJebLib\Simulations\SimPropellant.cs" />
-        <Compile Include="MechJebLib\Simulations\SimResource.cs" />
-        <Compile Include="MechJebLib\Simulations\SimVessel.cs" />
-        <Compile Include="MechJebLib\Utils\Check.cs" />
-        <Compile Include="MechJebLib\Utils\Logger.cs" />
-        <Compile Include="MechJebLib\Utils\ObjectPool.cs" />
-        <Compile Include="MechJebLib\Utils\Statics.cs" />
-        <Compile Include="MechJebLib\Utils\DictOfLists.cs" />
-        <Compile Include="MechJebModuleAirplaneAutopilot.cs" />
-        <Compile Include="MechJebModuleAirplaneGuidance.cs" />
-        <Compile Include="MechJebModuleAscentBaseAutopilot.cs" />
-        <Compile Include="MechJebModuleAscentClassicAutopilot.cs" />
-        <Compile Include="MechJebModuleAscentClassicPathMenu.cs" />
-        <Compile Include="MechJebModuleAscentGTAutopilot.cs" />
-        <Compile Include="MechJebModuleAscentMenu.cs" />
-        <Compile Include="MechJebModuleAscentPVGAutopilot.cs" />
-        <Compile Include="MechJebModuleAscentPVGSettingsMenu.cs" />
-        <Compile Include="MechJebModuleAscentSettings.cs" />
-        <Compile Include="MechJebModuleAscentSettingsMenu.cs" />
-        <Compile Include="MechJebModuleAttitudeAdjustment.cs" />
-        <Compile Include="MechJebModuleAttitudeController.cs" />
-        <Compile Include="MechJebModuleCustomInfoWindow.cs" />
-        <Compile Include="MechJebModuleDebugArrows.cs" />
-        <Compile Include="MechJebModuleDeployableAntennaController.cs" />
-        <Compile Include="MechJebModuleDeployableController.cs" />
-        <Compile Include="MechJebModuleDockingAutopilot.cs" />
-        <Compile Include="MechJebModuleDockingGuidance.cs" />
-        <Compile Include="MechJebModuleFlightRecorder.cs" />
-        <Compile Include="MechJebModuleFlightRecorderGraph.cs" />
-        <Compile Include="MechJebModuleInfoItems.cs" />
-        <Compile Include="MechJebModuleLandingAutopilot.cs" />
-        <Compile Include="MechJebModuleLandingGuidance.cs" />
-        <Compile Include="MechJebModuleLandingPredictions.cs" />
-        <Compile Include="MechJebModuleManeuverPlanner.cs" />
-        <Compile Include="MechJebModuleMenu.cs" />
-        <Compile Include="MechJebModuleStageStats.cs" />
-        <Compile Include="MechJebModuleNodeEditor.cs" />
-        <Compile Include="MechJebModuleNodeExecutor.cs" />
-        <Compile Include="MechJebModuleGuidanceController.cs" />
-        <Compile Include="MechJebModuleRCSBalancer.cs" />
-        <Compile Include="MechJebModuleRCSBalancerWindow.cs" />
-        <Compile Include="MechJebModuleRCSController.cs" />
-        <Compile Include="MechJebModuleRendezvousAutopilot.cs" />
-        <Compile Include="MechJebModuleRendezvousAutopilotWindow.cs" />
-        <Compile Include="MechJebModuleRendezvousGuidance.cs" />
-        <Compile Include="MechJebModuleRoverController.cs" />
-        <Compile Include="MechJebModuleRoverWindow.cs" />
-        <Compile Include="MechJebModuleSettings.cs" />
-        <Compile Include="MechJebModuleSmartASS.cs" />
-        <Compile Include="MechJebModuleSmartRcs.cs" />
-        <Compile Include="MechJebModuleSolarPanelController.cs" />
-        <Compile Include="MechJebModuleSpaceplaneAutopilot.cs" />
-        <Compile Include="MechJebModuleSpaceplaneGuidance.cs" />
-        <Compile Include="MechJebModuleSpinupController.cs" />
-        <Compile Include="MechJebModuleStageStatsOld.cs" />
-        <Compile Include="MechJebModuleStagingController.cs" />
-        <Compile Include="MechJebModuleSuicideTimer.cs" />
-        <Compile Include="MechJebModuleTargetController.cs" />
-        <Compile Include="MechJebModuleThrustController.cs" />
-        <Compile Include="MechJebModuleThrustWindow.cs" />
-        <Compile Include="MechJebModuleTranslatron.cs" />
-        <Compile Include="MechJebModuleWarpController.cs" />
-        <Compile Include="MechJebModuleWarpHelper.cs" />
-        <Compile Include="MechJebModuleWaypointWindow.cs" />
-        <Compile Include="MechjebBundlesManager.cs" />
-        <Compile Include="MechJebStageStatsHelper.cs" />
-        <Compile Include="ModExtensionDemo.cs" />
-        <Compile Include="MuUtils.cs" />
-        <Compile Include="OrbitExtensions.cs" />
-        <Compile Include="OrbitalManeuverCalculator.cs" />
-        <Compile Include="PIDController.cs" />
-        <Compile Include="PartExtensions.cs" />
-        <Compile Include="Properties\AssemblyInfo.cs" />
-        <Compile Include="Properties\Resources.Designer.cs" />
-        <Compile Include="MechJebModulePVGGlueBall.cs" />
-        <Compile Include="RCSSolver.cs" />
-        <Compile Include="ReentrySimulation.cs" />
-        <Compile Include="ReentrySimulation\SimCurves.cs" />
-        <Compile Include="ReflectionUtils.cs" />
-        <Compile Include="ToolbarWrapper.cs" />
-        <Compile Include="UnityToolbag\Dispatcher\Dispatcher.cs" />
-        <Compile Include="UnityToolbag\Future\Future.cs" />
-        <Compile Include="Vector6.cs" />
-        <Compile Include="VesselExtensions.cs" />
-        <Compile Include="VesselState.cs" />
-        <Compile Include="alglib\alglibinternal.cs" />
-        <Compile Include="alglib\alglibmisc.cs" />
-        <Compile Include="alglib\ap.cs" />
-        <Compile Include="alglib\dataanalysis.cs" />
-        <Compile Include="alglib\diffequations.cs" />
-        <Compile Include="alglib\fasttransforms.cs" />
-        <Compile Include="alglib\integration.cs" />
-        <Compile Include="alglib\interpolation.cs" />
-        <Compile Include="alglib\linalg.cs" />
-        <Compile Include="alglib\optimization.cs" />
-        <Compile Include="alglib\solvers.cs" />
-        <Compile Include="alglib\specialfunctions.cs" />
-        <Compile Include="alglib\statistics.cs" />
+        <Compile Include="AttitudeControllers\BaseAttitudeController.cs"/>
+        <Compile Include="AttitudeControllers\BetterController.cs"/>
+        <Compile Include="AttitudeControllers\HybridController.cs"/>
+        <Compile Include="AttitudeControllers\KosAttitudeController.cs"/>
+        <Compile Include="AttitudeControllers\MJAttitudeController.cs"/>
+        <Compile Include="AttitudeControllers\KosPIDLoop.cs"/>
+        <Compile Include="AttitudeControllers\TorquePI.cs"/>
+        <Compile Include="AutopilotModule.cs"/>
+        <Compile Include="CachedLocalizer.cs"/>
+        <Compile Include="CelestialBodyExtensions.cs"/>
+        <Compile Include="CompatibilityChecker.cs"/>
+        <Compile Include="ComputerModule.cs"/>
+        <Compile Include="DisplayModule.cs"/>
+        <Compile Include="FlyingSim\SimulatedParachute.cs"/>
+        <Compile Include="FlyingSim\SimulatedPart.cs"/>
+        <Compile Include="FlyingSim\SimulatedVessel.cs"/>
+        <Compile Include="FuelFlowSimulation.cs"/>
+        <Compile Include="FuelNode.cs"/>
+        <Compile Include="FuelStats.cs"/>
+        <Compile Include="GlobalSuppressions.cs"/>
+        <Compile Include="GLUtils.cs"/>
+        <Compile Include="GuiUtils.cs"/>
+        <Compile Include="InstallChecker.cs"/>
+        <Compile Include="LandingAutopilot\CoastToDeceleration.cs"/>
+        <Compile Include="LandingAutopilot\CourseCorrection.cs"/>
+        <Compile Include="LandingAutopilot\DecelerationBurn.cs"/>
+        <Compile Include="LandingAutopilot\DeorbitBurn.cs"/>
+        <Compile Include="LandingAutopilot\FinalDescent.cs"/>
+        <Compile Include="LandingAutopilot\KillHorizontalVelocity.cs"/>
+        <Compile Include="LandingAutopilot\LowDeorbitBurn.cs"/>
+        <Compile Include="LandingAutopilot\PlaneChange.cs"/>
+        <Compile Include="LandingAutopilot\UntargetedDeorbit.cs"/>
+        <Compile Include="Maneuver\Operation.cs"/>
+        <Compile Include="Maneuver\OperationAdvancedTransfer.cs"/>
+        <Compile Include="Maneuver\OperationApoapsis.cs"/>
+        <Compile Include="Maneuver\OperationCircularize.cs"/>
+        <Compile Include="Maneuver\OperationCourseCorrection.cs"/>
+        <Compile Include="Maneuver\OperationEccentricity.cs"/>
+        <Compile Include="Maneuver\OperationEllipticize.cs"/>
+        <Compile Include="Maneuver\OperationInclination.cs"/>
+        <Compile Include="Maneuver\OperationInterplanetaryTransfer.cs"/>
+        <Compile Include="Maneuver\OperationKillRelVel.cs"/>
+        <Compile Include="Maneuver\OperationLambert.cs"/>
+        <Compile Include="Maneuver\OperationLan.cs"/>
+        <Compile Include="Maneuver\OperationLongitude.cs"/>
+        <Compile Include="Maneuver\OperationMoonReturn.cs"/>
+        <Compile Include="Maneuver\OperationPeriapsis.cs"/>
+        <Compile Include="Maneuver\OperationPlane.cs"/>
+        <Compile Include="Maneuver\OperationResonantOrbit.cs"/>
+        <Compile Include="Maneuver\OperationSemiMajor.cs"/>
+        <Compile Include="Maneuver\OperationTransfer.cs"/>
+        <Compile Include="Maneuver\PlotArea.cs"/>
+        <Compile Include="Maneuver\Porkchop.cs"/>
+        <Compile Include="Maneuver\TimeSelector.cs"/>
+        <Compile Include="Maneuver\TransferCalculator.cs"/>
+        <Compile Include="MathExtensions.cs"/>
+        <Compile Include="MechJebAR202.cs"/>
+        <Compile Include="MechJebCore.cs"/>
+        <Compile Include="MechJebLib\Control\PIDLoop.cs"/>
+        <Compile Include="MechJebLib\Core\Bisection.cs"/>
+        <Compile Include="MechJebLib\Core\BrentMin.cs"/>
+        <Compile Include="MechJebLib\Core\BrentRoot.cs"/>
+        <Compile Include="MechJebLib\Core\FunctionImpls\RealDeltaVToChangeApoapsisPrograde.cs"/>
+        <Compile Include="MechJebLib\Core\FunctionImpls\RealSingleImpulseHyperbolicBurn.cs"/>
+        <Compile Include="MechJebLib\Core\Functions\Interpolants.cs"/>
+        <Compile Include="MechJebLib\Core\Functions\Maneuvers.cs"/>
+        <Compile Include="MechJebLib\Core\Maths.cs"/>
+        <Compile Include="MechJebLib\Core\Functions\Angles.cs"/>
+        <Compile Include="MechJebLib\Core\Gooding.cs"/>
+        <Compile Include="MechJebLib\Core\ODE\BS3.cs"/>
+        <Compile Include="MechJebLib\Core\ODE\DP5.cs"/>
+        <Compile Include="MechJebLib\Core\ODE\AbstractIVP.cs"/>
+        <Compile Include="MechJebLib\Core\ODE\AbstractRungeKutta.cs"/>
+        <Compile Include="MechJebLib\Core\ODE\Event.cs"/>
+        <Compile Include="MechJebLib\Core\TwoBody\Shepperd.cs"/>
+        <Compile Include="MechJebLib\Core\TwoBody\Farnocchia.cs"/>
+        <Compile Include="MechJebLib\Maneuvers\ChangeOrbitalElement.cs"/>
+        <Compile Include="MechJebLib\Maneuvers\ReturnFromMoon.cs"/>
+        <Compile Include="MechJebLib\Primitives\Dual.cs"/>
+        <Compile Include="MechJebLib\Primitives\DualV3.cs"/>
+        <Compile Include="MechJebLib\Primitives\Vn.cs"/>
+        <Compile Include="MechJebLib\Primitives\Scale.cs"/>
+        <Compile Include="MechJebLib\PVG\ContinuityLayout.cs"/>
+        <Compile Include="MechJebLib\PVG\InputLayout.cs"/>
+        <Compile Include="MechJebLib\PVG\OutputLayout.cs"/>
+        <Compile Include="MechJebLib\PVG\AscentBuilder.cs"/>
+        <Compile Include="MechJebLib\PVG\Integrators\IPVGIntegrator.cs"/>
+        <Compile Include="MechJebLib\PVG\Integrators\VacuumCoastAnalytic.cs"/>
+        <Compile Include="MechJebLib\PVG\Integrators\VacuumThrustAnalytic.cs"/>
+        <Compile Include="MechJebLib\PVG\Integrators\VacuumThrustIntegrator.cs"/>
+        <Compile Include="MechJebLib\PVG\Ascent.cs"/>
+        <Compile Include="MechJebLib\PVG\Phase.cs"/>
+        <Compile Include="MechJebLib\PVG\Problem.cs"/>
+        <Compile Include="MechJebLib\PVG\OptimizerBuilder.cs"/>
+        <Compile Include="MechJebLib\PVG\ResidualLayout.cs"/>
+        <Compile Include="MechJebLib\PVG\Solution.cs"/>
+        <Compile Include="MechJebLib\PVG\Optimizer.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle3Energy.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle4Energy.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle4Reduced.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle4Propellant.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\FlightPathAngle5Reduced.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\Intercept6Cartesian.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\IPVGTerminal.cs"/>
+        <Compile Include="MechJebLib\Primitives\H1.cs"/>
+        <Compile Include="MechJebLib\Primitives\H3.cs"/>
+        <Compile Include="MechJebLib\Primitives\HBase.cs"/>
+        <Compile Include="MechJebLib\Primitives\Hn.cs"/>
+        <Compile Include="MechJebLib\Primitives\M3.cs"/>
+        <Compile Include="MechJebLib\Primitives\Q3.cs"/>
+        <Compile Include="MechJebLib\Primitives\V3.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\Kepler3Reduced.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\Kepler4Reduced.cs"/>
+        <Compile Include="MechJebLib\PVG\Terminal\Kepler5Reduced.cs"/>
+        <Compile Include="MechJebLib\Simulations\SimVesselManager.cs"/>
+        <Compile Include="MechJebLib\Simulations\SimVesselUpdater.cs"/>
+        <Compile Include="MechJebLib\Suicide.cs"/>
+        <Compile Include="MechJebLib\SuicideBuilder.cs"/>
+        <Compile Include="MechJebLib\Utils\BackgroundJob.cs"/>
+        <Compile Include="MechJebLib\Simulations\SimVesselBuilder.cs"/>
+        <Compile Include="MechJebLib\Simulations\DecouplingAnalyzer.cs"/>
+        <Compile Include="MechJebLib\Simulations\FuelFlowSimulation.cs"/>
+        <Compile Include="MechJebLib\Simulations\FuelStats.cs"/>
+        <Compile Include="MechJebLib\Simulations\PartModules\SimModuleRCS.cs"/>
+        <Compile Include="MechJebLib\Simulations\SimPart.cs"/>
+        <Compile Include="MechJebLib\Simulations\SimPartModule.cs"/>
+        <Compile Include="MechJebLib\Simulations\PartModules\SimLaunchClamp.cs"/>
+        <Compile Include="MechJebLib\Simulations\PartModules\SimModuleDecouple.cs"/>
+        <Compile Include="MechJebLib\Simulations\PartModules\SimModuleDockingNode.cs"/>
+        <Compile Include="MechJebLib\Simulations\PartModules\SimModuleEngines.cs"/>
+        <Compile Include="MechJebLib\Simulations\PartModules\SimProceduralFairingDecoupler.cs"/>
+        <Compile Include="MechJebLib\Simulations\SimPropellant.cs"/>
+        <Compile Include="MechJebLib\Simulations\SimResource.cs"/>
+        <Compile Include="MechJebLib\Simulations\SimVessel.cs"/>
+        <Compile Include="MechJebLib\Utils\Check.cs"/>
+        <Compile Include="MechJebLib\Utils\Logger.cs"/>
+        <Compile Include="MechJebLib\Utils\ObjectPool.cs"/>
+        <Compile Include="MechJebLib\Utils\Statics.cs"/>
+        <Compile Include="MechJebLib\Utils\DictOfLists.cs"/>
+        <Compile Include="MechJebModuleAirplaneAutopilot.cs"/>
+        <Compile Include="MechJebModuleAirplaneGuidance.cs"/>
+        <Compile Include="MechJebModuleAscentBaseAutopilot.cs"/>
+        <Compile Include="MechJebModuleAscentClassicAutopilot.cs"/>
+        <Compile Include="MechJebModuleAscentClassicPathMenu.cs"/>
+        <Compile Include="MechJebModuleAscentGTAutopilot.cs"/>
+        <Compile Include="MechJebModuleAscentMenu.cs"/>
+        <Compile Include="MechJebModuleAscentPVGAutopilot.cs"/>
+        <Compile Include="MechJebModuleAscentPVGSettingsMenu.cs"/>
+        <Compile Include="MechJebModuleAscentSettings.cs"/>
+        <Compile Include="MechJebModuleAscentSettingsMenu.cs"/>
+        <Compile Include="MechJebModuleAttitudeAdjustment.cs"/>
+        <Compile Include="MechJebModuleAttitudeController.cs"/>
+        <Compile Include="MechJebModuleCustomInfoWindow.cs"/>
+        <Compile Include="MechJebModuleDebugArrows.cs"/>
+        <Compile Include="MechJebModuleDeployableAntennaController.cs"/>
+        <Compile Include="MechJebModuleDeployableController.cs"/>
+        <Compile Include="MechJebModuleDockingAutopilot.cs"/>
+        <Compile Include="MechJebModuleDockingGuidance.cs"/>
+        <Compile Include="MechJebModuleFlightRecorder.cs"/>
+        <Compile Include="MechJebModuleFlightRecorderGraph.cs"/>
+        <Compile Include="MechJebModuleInfoItems.cs"/>
+        <Compile Include="MechJebModuleLandingAutopilot.cs"/>
+        <Compile Include="MechJebModuleLandingGuidance.cs"/>
+        <Compile Include="MechJebModuleLandingPredictions.cs"/>
+        <Compile Include="MechJebModuleManeuverPlanner.cs"/>
+        <Compile Include="MechJebModuleMenu.cs"/>
+        <Compile Include="MechJebModuleStageStats.cs"/>
+        <Compile Include="MechJebModuleNodeEditor.cs"/>
+        <Compile Include="MechJebModuleNodeExecutor.cs"/>
+        <Compile Include="MechJebModuleGuidanceController.cs"/>
+        <Compile Include="MechJebModuleRCSBalancer.cs"/>
+        <Compile Include="MechJebModuleRCSBalancerWindow.cs"/>
+        <Compile Include="MechJebModuleRCSController.cs"/>
+        <Compile Include="MechJebModuleRendezvousAutopilot.cs"/>
+        <Compile Include="MechJebModuleRendezvousAutopilotWindow.cs"/>
+        <Compile Include="MechJebModuleRendezvousGuidance.cs"/>
+        <Compile Include="MechJebModuleRoverController.cs"/>
+        <Compile Include="MechJebModuleRoverWindow.cs"/>
+        <Compile Include="MechJebModuleSettings.cs"/>
+        <Compile Include="MechJebModuleSmartASS.cs"/>
+        <Compile Include="MechJebModuleSmartRcs.cs"/>
+        <Compile Include="MechJebModuleSolarPanelController.cs"/>
+        <Compile Include="MechJebModuleSpaceplaneAutopilot.cs"/>
+        <Compile Include="MechJebModuleSpaceplaneGuidance.cs"/>
+        <Compile Include="MechJebModuleSpinupController.cs"/>
+        <Compile Include="MechJebModuleStageStatsOld.cs"/>
+        <Compile Include="MechJebModuleStagingController.cs"/>
+        <Compile Include="MechJebModuleSuicideTimer.cs"/>
+        <Compile Include="MechJebModuleTargetController.cs"/>
+        <Compile Include="MechJebModuleThrustController.cs"/>
+        <Compile Include="MechJebModuleThrustWindow.cs"/>
+        <Compile Include="MechJebModuleTranslatron.cs"/>
+        <Compile Include="MechJebModuleWarpController.cs"/>
+        <Compile Include="MechJebModuleWarpHelper.cs"/>
+        <Compile Include="MechJebModuleWaypointWindow.cs"/>
+        <Compile Include="MechjebBundlesManager.cs"/>
+        <Compile Include="MechJebStageStatsHelper.cs"/>
+        <Compile Include="ModExtensionDemo.cs"/>
+        <Compile Include="MuUtils.cs"/>
+        <Compile Include="OrbitExtensions.cs"/>
+        <Compile Include="OrbitalManeuverCalculator.cs"/>
+        <Compile Include="PIDController.cs"/>
+        <Compile Include="PartExtensions.cs"/>
+        <Compile Include="Properties\AssemblyInfo.cs"/>
+        <Compile Include="Properties\Resources.Designer.cs"/>
+        <Compile Include="MechJebModulePVGGlueBall.cs"/>
+        <Compile Include="RCSSolver.cs"/>
+        <Compile Include="ReentrySimulation.cs"/>
+        <Compile Include="ReentrySimulation\SimCurves.cs"/>
+        <Compile Include="ReflectionUtils.cs"/>
+        <Compile Include="ToolbarWrapper.cs"/>
+        <Compile Include="UnityToolbag\Dispatcher\Dispatcher.cs"/>
+        <Compile Include="UnityToolbag\Future\Future.cs"/>
+        <Compile Include="Vector6.cs"/>
+        <Compile Include="VesselExtensions.cs"/>
+        <Compile Include="VesselState.cs"/>
+        <Compile Include="alglib\alglibinternal.cs"/>
+        <Compile Include="alglib\alglibmisc.cs"/>
+        <Compile Include="alglib\ap.cs"/>
+        <Compile Include="alglib\dataanalysis.cs"/>
+        <Compile Include="alglib\diffequations.cs"/>
+        <Compile Include="alglib\fasttransforms.cs"/>
+        <Compile Include="alglib\integration.cs"/>
+        <Compile Include="alglib\interpolation.cs"/>
+        <Compile Include="alglib\linalg.cs"/>
+        <Compile Include="alglib\optimization.cs"/>
+        <Compile Include="alglib\solvers.cs"/>
+        <Compile Include="alglib\specialfunctions.cs"/>
+        <Compile Include="alglib\statistics.cs"/>
     </ItemGroup>
     <ItemGroup>
-        <EmbeddedResource Include="Properties\Resources.resx" />
+        <EmbeddedResource Include="Properties\Resources.resx"/>
     </ItemGroup>
     <ItemGroup>
-        <None Include="copy_build.bat" />
-        <None Include="copy_build.sh" />
-        <None Include="Properties\shader" />
-        <None Include="Properties\shader2" />
-        <None Include="Properties\shader3" />
-        <None Include="UnityToolbag\Dispatcher\README.md" />
-        <None Include="UnityToolbag\Future\README.md" />
+        <None Include="copy_build.bat"/>
+        <None Include="copy_build.sh"/>
+        <None Include="Properties\shader"/>
+        <None Include="Properties\shader2"/>
+        <None Include="Properties\shader3"/>
+        <None Include="UnityToolbag\Dispatcher\README.md"/>
+        <None Include="UnityToolbag\Future\README.md"/>
     </ItemGroup>
     <ItemGroup>
         <Reference Include="Assembly-CSharp, Version=0.0.0.0, Culture=neutral, processorArchitecture=MSIL">
@@ -340,12 +342,12 @@
             <Private>False</Private>
         </Reference>
     </ItemGroup>
-    <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
+    <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets"/>
     <Target Name="AfterBuild" Condition=" '$(OS)' == 'Windows_NT' ">
-        <Exec Command="call &quot;$(ProjectDir)copy_build.bat&quot; &quot;$(TargetPath)&quot; &quot;$(TargetDir)&quot; &quot;$(TargetName)&quot; &quot;$(ProjectDir)&quot;" />
+        <Exec Command="call &quot;$(ProjectDir)copy_build.bat&quot; &quot;$(TargetPath)&quot; &quot;$(TargetDir)&quot; &quot;$(TargetName)&quot; &quot;$(ProjectDir)&quot;"/>
     </Target>
     <Target Name="AfterBuild" Condition=" '$(OS)' != 'Windows_NT' ">
-        <Exec Command="'$(ProjectDir)/copy_build.sh' '$(TargetPath)' '$(TargetDir)' '$(TargetName)' '$(ProjectDir)' '$(ReferencePath)'" />
+        <Exec Command="'$(ProjectDir)/copy_build.sh' '$(TargetPath)' '$(TargetDir)' '$(TargetName)' '$(ProjectDir)' '$(ReferencePath)'"/>
     </Target>
     <!-- To modify your build process, add your task inside one of the targets below and uncomment it.
          Other similar extension points exist, see Microsoft.Common.targets.
diff --git a/MechJeb2/MechJebLib/Core/Maths.cs b/MechJeb2/MechJebLib/Core/Maths.cs
index 65f3c09f..d510892e 100644
--- a/MechJeb2/MechJebLib/Core/Maths.cs
+++ b/MechJeb2/MechJebLib/Core/Maths.cs
@@ -78,14 +78,10 @@ public static (double vT, double gammaT) ConvertApsidesTargetToFPA(double peR, d
         public static double CircularVelocity(double mu, double r) => Sqrt(mu / r);
 
         public static double PeriapsisFromKeplerian(double sma, double ecc) => sma * (1 - ecc);
+        public static Dual   PeriapsisFromKeplerian(Dual sma, Dual ecc)     => sma * (1 - ecc);
 
-        public static double ApoapsisFromKeplerian(double sma, double ecc, bool hyperbolic = true)
-        {
-            double apo = sma * (1 + ecc);
-            if (apo >= 0)
-                return apo;
-            return hyperbolic ? apo : double.MaxValue;
-        }
+        public static double ApoapsisFromKeplerian(double sma, double ecc) => sma * (1 + ecc);
+        public static Dual   ApoapsisFromKeplerian(Dual sma, Dual ecc)     => sma * (1 + ecc);
 
         public static double PeriapsisFromStateVectors(double mu, V3 r, V3 v)
         {
@@ -94,11 +90,25 @@ public static double PeriapsisFromStateVectors(double mu, V3 r, V3 v)
             return PeriapsisFromKeplerian(sma, ecc);
         }
 
-        public static double ApoapsisFromStateVectors(double mu, V3 r, V3 v, bool hyperbolic = true)
+        public static Dual PeriapsisFromStateVectors(Dual mu, DualV3 r, DualV3 v)
+        {
+            Dual sma, ecc;
+            (sma, ecc) = SmaEccFromStateVectors(mu, r, v);
+            return PeriapsisFromKeplerian(sma, ecc);
+        }
+
+        public static double ApoapsisFromStateVectors(double mu, V3 r, V3 v)
         {
             double sma, ecc;
             (sma, ecc) = SmaEccFromStateVectors(mu, r, v);
-            return ApoapsisFromKeplerian(sma, ecc, hyperbolic);
+            return ApoapsisFromKeplerian(sma, ecc);
+        }
+
+        public static Dual ApoapsisFromStateVectors(Dual mu, DualV3 r, DualV3 v)
+        {
+            Dual sma, ecc;
+            (sma, ecc) = SmaEccFromStateVectors(mu, r, v);
+            return ApoapsisFromKeplerian(sma, ecc);
         }
 
         public static double EccFromStateVectors(double mu, V3 r, V3 v)
@@ -107,6 +117,12 @@ public static double EccFromStateVectors(double mu, V3 r, V3 v)
             return eccvec.magnitude;
         }
 
+        public static Dual EccFromStateVectors(Dual mu, DualV3 r, DualV3 v)
+        {
+            DualV3 eccvec = DualV3.Cross(v / mu, DualV3.Cross(r, v)) - r.normalized;
+            return eccvec.magnitude;
+        }
+
         public static (double sma, double ecc) SmaEccFromStateVectors(double mu, V3 r, V3 v)
         {
             var h = V3.Cross(r, v);
@@ -114,8 +130,17 @@ public static (double sma, double ecc) SmaEccFromStateVectors(double mu, V3 r, V
             return (sma, Sqrt(Max(1 - h.sqrMagnitude / (sma * mu), 0)));
         }
 
+        public static (Dual sma, Dual ecc) SmaEccFromStateVectors(Dual mu, DualV3 r, DualV3 v)
+        {
+            var h = DualV3.Cross(r, v);
+            Dual sma = SmaFromStateVectors(mu, r, v);
+            return (sma, Dual.Sqrt(Dual.Max(1 - h.sqrMagnitude / (sma * mu), 0)));
+        }
+
         public static double SmaFromStateVectors(double mu, V3 r, V3 v) => mu / (2.0 * mu / r.magnitude - V3.Dot(v, v));
 
+        public static Dual SmaFromStateVectors(Dual mu, DualV3 r, DualV3 v) => mu / (2.0 * mu / r.magnitude - DualV3.Dot(v, v));
+
         public static double IncFromStateVectors(V3 r, V3 v)
         {
             V3 hhat = V3.Cross(r, v).normalized;
diff --git a/MechJeb2/MechJebLib/Maneuvers/ChangeOrbitalElement.cs b/MechJeb2/MechJebLib/Maneuvers/ChangeOrbitalElement.cs
index c90bcefe..39377374 100644
--- a/MechJeb2/MechJebLib/Maneuvers/ChangeOrbitalElement.cs
+++ b/MechJeb2/MechJebLib/Maneuvers/ChangeOrbitalElement.cs
@@ -25,6 +25,57 @@ private struct Args
             public Type   Type;
         }
 
+        private static void NLPFunction2(double[] x, double[] fi, double[,] jac, object obj)
+        {
+            var dv0 = new DualV3(x[0], x[1], 0, 1, 0, 0);
+            var dv1 = new DualV3(x[0], x[1], 0, 0, 1, 0);
+
+            var args = (Args)obj;
+            V3 p = args.P;
+            V3 q = args.Q;
+            double value = args.Value;
+            Type type = args.Type;
+
+            Dual sqM0 = dv0.sqrMagnitude;
+            Dual sqM1 = dv1.sqrMagnitude;
+
+            fi[0]     = sqM0.M;
+            jac[0, 0] = sqM0.D;
+            jac[0, 1] = sqM1.D;
+
+            switch (type)
+            {
+                case Type.PERIAPSIS:
+                    Dual peR0 = Maths.PeriapsisFromStateVectors(1.0, p, q + dv0) - value;
+                    Dual peR1 = Maths.PeriapsisFromStateVectors(1.0, p, q + dv1) - value;
+                    fi[1]     = peR0.M;
+                    jac[1, 0] = peR0.D;
+                    jac[1, 1] = peR1.D;
+                    break;
+                case Type.APOAPSIS:
+                    Dual apR0 = 1.0 / Maths.ApoapsisFromStateVectors(1.0, p, q + dv0) - 1.0 / value;
+                    Dual apR1 = 1.0 / Maths.ApoapsisFromStateVectors(1.0, p, q + dv1) - 1.0 / value;
+                    fi[1]     = apR0.M;
+                    jac[1, 0] = apR0.D;
+                    jac[1, 1] = apR1.D;
+                    break;
+                case Type.SMA:
+                    Dual sma0 = 1.0 / Maths.SmaFromStateVectors(1.0, p, q + dv0) - 1.0 / value;
+                    Dual sma1 = 1.0 / Maths.SmaFromStateVectors(1.0, p, q + dv1) - 1.0 / value;
+                    fi[1]     = sma0.M;
+                    jac[1, 0] = sma0.D;
+                    jac[1, 1] = sma1.D;
+                    break;
+                case Type.ECC:
+                    Dual ecc0 = Maths.EccFromStateVectors(1.0, p, q + dv0) - value;
+                    Dual ecc1 = Maths.EccFromStateVectors(1.0, p, q + dv1) - value;
+                    fi[1]     = ecc0.M;
+                    jac[1, 0] = ecc0.D;
+                    jac[1, 1] = ecc1.D;
+                    break;
+            }
+        }
+
         private static void NLPFunction(double[] x, double[] fi, object obj)
         {
             var dv = new V3(x[0], x[1], 0);
@@ -36,6 +87,7 @@ private static void NLPFunction(double[] x, double[] fi, object obj)
             Type type = args.Type;
 
             fi[0] = dv.sqrMagnitude;
+
             switch (type)
             {
                 case Type.PERIAPSIS:
@@ -54,7 +106,7 @@ private static void NLPFunction(double[] x, double[] fi, object obj)
             }
         }
 
-        private static V3 DeltaV(double mu, V3 r, V3 v, double value, Type type)
+        private static V3 DeltaV(double mu, V3 r, V3 v, double value, Type type, bool optguard=false)
         {
             if (!mu.IsFinite())
                 throw new ArgumentException("bad mu in ChangeOrbitalElement");
@@ -97,52 +149,65 @@ private static V3 DeltaV(double mu, V3 r, V3 v, double value, Type type)
 
             var args = new Args { P = p, Q = q, Value = type == Type.ECC ? value : value / scale.LengthScale, Type = type };
 
-            alglib.minnlccreatef(NVARIABLES, x, DIFFSTEP, out alglib.minnlcstate state);
+            alglib.minnlccreate(NVARIABLES, x, out alglib.minnlcstate state);
             alglib.minnlcsetalgosqp(state);
             alglib.minnlcsetcond(state, EPSX, MAXITS);
             alglib.minnlcsetnlc(state, NEQUALITYCONSTRAINTS, NINEQUALITYCONSTRAINTS);
 
-            alglib.minnlcoptimize(state, NLPFunction, null, args);
+            if (optguard)
+            {
+                alglib.minnlcoptguardsmoothness(state);
+                alglib.minnlcoptguardgradient(state, DIFFSTEP);
+            }
+
+            alglib.minnlcoptimize(state, NLPFunction2, null, args);
             alglib.minnlcresults(state, out x, out alglib.minnlcreport rep);
 
             if (rep.terminationtype < 0)
                 throw new Exception(
-                    $"DeltaVToChangeApsis({mu}, {r}, {v}, {value}, {type}): SQP solver terminated abnormally: {rep.terminationtype}"
+                    $"ChangeOrbitalElement.DeltaV({mu}, {r}, {v}, {value}, {type}): SQP solver terminated abnormally: {rep.terminationtype}"
                 );
 
+            if (optguard)
+            {
+                alglib.minnlcoptguardresults(state, out alglib.optguardreport ogrep);
+                if (ogrep.badgradsuspected || ogrep.nonc0suspected || ogrep.nonc1suspected)
+                    throw new Exception("alglib optguard caught an error, i should report better on errors now");
+            }
+
             return rot * new V3(x[0], x[1], 0) * scale.VelocityScale;
         }
 
-        public static V3 ChangePeriapsis(double mu, V3 r, V3 v, double peR)
+        public static V3 ChangePeriapsis(double mu, V3 r, V3 v, double peR, bool optguard = false)
         {
             if (peR < 0 || (peR > r.magnitude) | !peR.IsFinite())
                 throw new ArgumentException($"Bad periapsis in ChangeOrbitalElement = {peR}");
 
-            return DeltaV(mu, r, v, peR, Type.PERIAPSIS);
+            return DeltaV(mu, r, v, peR, Type.PERIAPSIS, optguard);
         }
 
-        public static V3 ChangeApoapsis(double mu, V3 r, V3 v, double apR)
+        public static V3 ChangeApoapsis(double mu, V3 r, V3 v, double apR, bool optguard = false)
         {
             if (!apR.IsFinite() || (apR > 0 && apR < r.magnitude))
                 throw new ArgumentException($"Bad apoapsis in ChangeOrbitalElement = {apR}");
 
-            return DeltaV(mu, r, v, apR, Type.APOAPSIS);
+            return DeltaV(mu, r, v, apR, Type.APOAPSIS, optguard);
         }
 
-        public static V3 ChangeSMA(double mu, V3 r, V3 v, double sma)
+        public static V3 ChangeSMA(double mu, V3 r, V3 v, double sma, bool optguard = false)
         {
             if (!sma.IsFinite())
                 throw new ArgumentException($"Bad SMA in ChangeOrbitalElement = {sma}");
 
-            return DeltaV(mu, r, v, sma, Type.SMA);
+            return DeltaV(mu, r, v, sma, Type.SMA, optguard);
         }
 
-        public static V3 ChangeECC(double mu, V3 r, V3 v, double ecc)
+        public static V3 ChangeECC(double mu, V3 r, V3 v, double ecc, bool optguard = false)
         {
             if (!ecc.IsFinite() || ecc < 0)
                 throw new ArgumentException($"Bad Ecc in ChangeOrbitalElement = {ecc}");
 
-            return DeltaV(mu, r, v, ecc, Type.ECC);
+            return DeltaV(mu, r, v, ecc, Type.ECC, optguard);
         }
     }
 }
diff --git a/MechJeb2/MechJebLib/Primitives/Dual.cs b/MechJeb2/MechJebLib/Primitives/Dual.cs
new file mode 100644
index 00000000..789ed557
--- /dev/null
+++ b/MechJeb2/MechJebLib/Primitives/Dual.cs
@@ -0,0 +1,67 @@
+/*
+ * Copyright Lamont Granquist, Sebastien Gaggini and the MechJeb contributors
+ * SPDX-License-Identifier: LicenseRef-PD-hp OR Unlicense OR CC0-1.0 OR 0BSD OR MIT-0 OR MIT OR LGPL-2.1+
+ */
+
+#nullable enable
+
+using System;
+using System.Globalization;
+using MechJebLib.Utils;
+
+namespace MechJebLib.Primitives
+{
+    public class Dual : IEquatable<Dual>, IComparable<Dual>, IFormattable
+    {
+        public readonly double M;
+        public readonly double D;
+
+        public Dual(double m, double d = 0)
+        {
+            M = m;
+            D = d;
+        }
+
+        public static Dual Sin(Dual d) => new Dual(Math.Sin(d.M), Math.Cos(d.M) * d.D);
+        public static Dual Cos(Dual d) => new Dual(Math.Cos(d.M), -Math.Sin(d.M) * d.D);
+
+        public static Dual Tan(Dual d)
+        {
+            double t = Math.Tan(d.M);
+            return new Dual(t, (1.0 + t * t) * d.D);
+        }
+
+        public static Dual Log(Dual d)         => new Dual(Math.Log(d.M), 1 / d.M * d.D);
+        public static Dual Powi(Dual d, int k) => new Dual(Statics.Powi(d.M, k), k * Statics.Powi(d.M, k - 1) * d.D);
+        public static Dual Abs(Dual d)         => new Dual(Math.Abs(d.M), (d.M < 0 ? -1 : 1) * d.D);
+        public static Dual Exp(Dual d)         => new Dual(Math.Exp(d.M), Math.Exp(d.M) * d.D);
+        public static Dual Sqrt(Dual d)        => new Dual(Math.Sqrt(d.M), 1.0 / (2 * Math.Sqrt(d.M)) * d.D);
+        public static Dual Max(Dual d, int i)  => new Dual(Math.Max(d.M, i), d.M > i ? d.D : 0);
+
+        public static Dual operator -(Dual x)             => new Dual(-x.M, -x.D);
+        public static Dual operator +(Dual lhs, Dual rhs) => new Dual(lhs.M + rhs.M, lhs.D + rhs.D);
+        public static Dual operator -(Dual lhs, Dual rhs) => new Dual(lhs.M - rhs.M, lhs.D - rhs.D);
+        public static Dual operator *(Dual lhs, Dual rhs) => new Dual(lhs.M * rhs.M, lhs.D * rhs.M + rhs.D * lhs.M);
+        public static Dual operator /(Dual lhs, Dual rhs) => new Dual(lhs.M / rhs.M, (lhs.D * rhs.M - lhs.M * rhs.D) / (rhs.M * rhs.M));
+
+        public static explicit operator double(Dual d) => d.M;
+        public static implicit operator Dual(double d) => new Dual(d);
+
+        // ReSharper disable once CompareOfFloatsByEqualityOperator
+        public bool Equals(Dual other) => M == other.M && D.Equals(other.D);
+
+        public int CompareTo(Dual other) => M.CompareTo(other.M);
+
+        public override string ToString() => ToString(null, CultureInfo.InvariantCulture.NumberFormat);
+
+        public string ToString(string? format) => ToString(format, CultureInfo.InvariantCulture.NumberFormat);
+
+        public string ToString(string? format, IFormatProvider formatProvider)
+        {
+            if (string.IsNullOrEmpty(format))
+                format = "G";
+            return
+                $"{M.ToString(format, formatProvider)} + {D.ToString(format, formatProvider)}ϵ";
+        }
+    }
+}
diff --git a/MechJeb2/MechJebLib/Primitives/DualV3.cs b/MechJeb2/MechJebLib/Primitives/DualV3.cs
new file mode 100644
index 00000000..eda3b741
--- /dev/null
+++ b/MechJeb2/MechJebLib/Primitives/DualV3.cs
@@ -0,0 +1,62 @@
+/*
+ * Copyright Lamont Granquist, Sebastien Gaggini and the MechJeb contributors
+ * SPDX-License-Identifier: LicenseRef-PD-hp OR Unlicense OR CC0-1.0 OR 0BSD OR MIT-0 OR MIT OR LGPL-2.1+
+ */
+
+#nullable enable
+
+using System;
+
+namespace MechJebLib.Primitives
+{
+    public class DualV3 : IEquatable<DualV3>, IComparable<DualV3>, IFormattable
+    {
+        public readonly V3 M;
+        public readonly V3 D;
+
+        public Dual x => new Dual(M.x, D.x);
+        public Dual y => new Dual(M.y, D.y);
+        public Dual z => new Dual(M.z, D.z);
+
+        private DualV3(V3 m, V3? dx = null)
+        {
+            M = m;
+            D = dx ?? V3.zero;
+        }
+
+        public DualV3(Dual x, Dual y, Dual z) : this(x.M, y.M, z.M, x.D, y.D, z.D) { }
+        public DualV3(double mx, double my, double mz, double dx, double dy, double dz) : this(new V3(mx, my, mz), new V3(dx, dy, dz)) { }
+
+        public Dual   sqrMagnitude => x * x + y * y + z * z;
+        public Dual   magnitude    => Dual.Sqrt(x * x + y * y + z * z);
+        public DualV3 normalized   => this / magnitude;
+
+        public static DualV3 operator +(DualV3 a, DualV3 b) => new DualV3(a.x + b.x, a.y + b.y, a.z + b.z);
+
+        public static DualV3 operator -(DualV3 a, DualV3 b) => new DualV3(a.x - b.x, a.y - b.y, a.z - b.z);
+
+        public static DualV3 operator *(DualV3 a, DualV3 b) => new DualV3(a.x * b.x, a.y * b.y, a.z * b.z);
+
+        public static DualV3 operator /(DualV3 a, DualV3 b) => new DualV3(a.x / b.x, a.y / b.y, a.z / b.z);
+
+        public static DualV3 operator -(DualV3 a) => new DualV3(-a.x, -a.y, -a.z);
+
+        public static DualV3 operator *(DualV3 a, Dual d) => new DualV3(a.x * d, a.y * d, a.z * d);
+
+        public static DualV3 operator *(Dual d, DualV3 a) => new DualV3(a.x * d, a.y * d, a.z * d);
+
+        public static DualV3 operator /(DualV3 a, Dual d) => new DualV3(a.x / d, a.y / d, a.z / d);
+
+        public static explicit operator V3(DualV3 d) => d.M;
+        public static implicit operator DualV3(V3 d) => new DualV3(d);
+
+        public bool   Equals(DualV3 other)                                    => throw new NotImplementedException();
+        public int    CompareTo(DualV3 other)                                 => throw new NotImplementedException();
+        public string ToString(string format, IFormatProvider formatProvider) => throw new NotImplementedException();
+
+        public static DualV3 Cross(DualV3 v1, DualV3 v2) =>
+            new DualV3(v1.y * v2.z - v1.z * v2.y, v1.z * v2.x - v1.x * v2.z, v1.x * v2.y - v1.y * v2.x);
+
+        public static Dual Dot(DualV3 v1, DualV3 v2) => v1.x * v2.x + v1.y * v2.y + v1.z * v2.z;
+    }
+}
diff --git a/MechJebLibTest/Maths/FunctionsTests.cs b/MechJebLibTest/Maths/FunctionsTests.cs
index a0425770..ec7982cb 100644
--- a/MechJebLibTest/Maths/FunctionsTests.cs
+++ b/MechJebLibTest/Maths/FunctionsTests.cs
@@ -806,7 +806,7 @@ private void ChangeOrbitalElementTest()
                 newR *= rscale;
                 double mu = rscale * vscale * vscale;
 
-                V3 dv = ChangeOrbitalElement.ChangePeriapsis(mu, r, v, newR);
+                V3 dv = ChangeOrbitalElement.ChangePeriapsis(mu, r, v, newR, true);
                 MechJebLib.Core.Maths.PeriapsisFromStateVectors(mu, r, v + dv).ShouldEqual(newR, 1e-9);
 
                 // validate this API works left handed.
@@ -815,12 +815,12 @@ private void ChangeOrbitalElementTest()
 
                 // now test apoapsis changing to elliptical
                 newR = random.NextDouble() * rscale * 1e9 + r.magnitude;
-                V3 dv3 = ChangeOrbitalElement.ChangeApoapsis(mu, r, v, newR);
+                V3 dv3 = ChangeOrbitalElement.ChangeApoapsis(mu, r, v, newR, true);
                 MechJebLib.Core.Maths.ApoapsisFromStateVectors(mu, r, v + dv3).ShouldEqual(newR, 1e-5);
 
                 // now test apoapsis changing to hyperbolic
                 newR = -(random.NextDouble() * 1e9 + 1e3) * rscale;
-                V3 dv4 = ChangeOrbitalElement.ChangeApoapsis(mu, r, v, newR);
+                V3 dv4 = ChangeOrbitalElement.ChangeApoapsis(mu, r, v, newR, true);
                 MechJebLib.Core.Maths.ApoapsisFromStateVectors(mu, r, v + dv4).ShouldEqual(newR, 1e-5);
 
                 // now test changing the SMA.
@@ -831,7 +831,7 @@ private void ChangeOrbitalElementTest()
                 v    = new V3(23370.6359939819, 12558.3695536628, 17864.1347044172);
                 newR = 35354091.544774853;
                 */
-                V3 dv5 = ChangeOrbitalElement.ChangeSMA(mu, r, v, newR);
+                V3 dv5 = ChangeOrbitalElement.ChangeSMA(mu, r, v, newR, true);
                 MechJebLib.Core.Maths.SmaFromStateVectors(mu, r, v + dv5).ShouldEqual(newR, 1e-9);
 
                 // now test changing the Ecc