h&FM8A      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                                                                                                                                                                                     (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred ?  LPFP-coreGiven a step size, a y-intercept, and a function, return a function with the given y-intercept whose derivative is the given function.  LPFP-coreGiven a step size, a function, a lower limit, and an upper limit, return the definite integral of the function.  (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred`% LPFP-core%A type for three-dimensional vectors. LPFP-corex component of a vector  LPFP-corey component of a vector! LPFP-corez component of a vector0 LPFP-core"An approximation to a real number.1 LPFP-coreAcceleration is a vector.2 LPFP-coreVelocity is a vector.3 LPFP-core:The position of a particle can be represented as a vector.4 LPFP-coreTime is a real number.5 LPFP-coreA derivative takes a real-valued function of a real variable (often time) as input, and produces a real-valued function of a real variable as output.6 LPFP-coreA vector derivative takes a vector-valued function of a real variable (usually time) as input, and produces a vector-valued function of a real variable as output.7 LPFP-coreGiven a step size, calculate the vector derivative of a vector-valued function of a real variable (usually time).: LPFP-coreGiven a step size, calculate the derivative of a real-valued function of a real variable (often time).; LPFP-coreGiven a time step and a position function, return a velocity function.< LPFP-coreGiven a time step and a velocity function, return an acceleration function.= LPFP-coreGiven initial position and a constant velocity, return a position function.> LPFP-coreGiven initial velocity and a constant acceleration, return a velocity function.? LPFP-coreGiven initial position, initial velocity, and a constant acceleration, return a position function.@ LPFP-coreGiven a nonzero velocity and an acceleration, return the component of acceleration parallel to the velocity.A LPFP-coreGiven a nonzero velocity and an acceleration, return the component of acceleration perpendicular to the velocity.B LPFP-coreGiven velocity and acceleration, return the rate at which speed is changing.I LPFP-core3Form a vector by giving its x, y, and z components.J LPFP-core!A unit vector in the x direction.K LPFP-core!A unit vector in the y direction.L LPFP-core!A unit vector in the z direction.M LPFP-coreThe zero vector.N LPFP-coreNegate a vector.O LPFP-coreVector addition.P LPFP-coreVector subtraction.Q LPFP-coreAdd a list of vectors.R LPFP-core/Scalar multiplication of a number and a vector.S LPFP-core/Scalar multiplication of a vector and a number.T LPFP-coreDot product of two vectors.U LPFP-coreCross product of two vectors.V LPFP-core!Division of a vector by a number.W LPFP-coreMagnitude of a vector.X LPFP-core?Definite integral of a vector-valued function of a real number.; LPFP-coredt LPFP-coreposition function LPFP-corevelocity functionI LPFP-core x component LPFP-core y component LPFP-core z componentX LPFP-core step size dt LPFP-corevector-valued function LPFP-core lower limit LPFP-core upper limit LPFP-coreresult! "$#%'&(+*),-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`a67895:4321;<=>?@ABCD0./,-E(+*)FG%'&"$#! HIJKLMNOPQRSTUVWXYZ[\]^_`aO6P6R7S7T7U7V7(c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred o LPFP-coreA type class that expresses a relationship between a state space and a time-derivative-state space.q LPFP-coreA real vector space allows vector addition and scalar multiplication by reals.t LPFP-coreA numerical method turns a differential equation into a state-update function.u LPFP-coreA differential equation takes a state as input and returns as output the rate at which the state is changing.v LPFP-coreAn update function takes a state as input and returns an updated state as output. LPFP-coreGiven a numerical method, a differential equation, and an initial state, return a list of states. LPFP-coreGiven a step size, return the numerical method that uses the Euler method with that step size. LPFP-coreGiven a step size, return the numerical method that uses the 4th order Runge Kutta method with that step size. LPFP-core0A triple of real numbers is a real vector space. LPFP-core?A triple of real numbers can serve as the time derivative of a w.,nopqsrtuvwxyz{|}~,}|{zyxw~vutqsropn(c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred' LPFP-core6Data type for the time-derivative of a particle state. LPFP-coreData type for a one-body force. LPFP-coreData type for the state of a single particle in three-dimensional space. LPFP-coreA default particle state. LPFP-coreGiven a list of forces, return a differential equation based on Newton's second law. LPFP-coreThe force of gravity near Earth's surface. The z direction is toward the sky. Assumes SI units. LPFP-coreThe force of the Sun's gravity on an object. The origin is at center of the Sun. Assumes SI units. LPFP-core)The force of air resistance on an object. LPFP-coreThe force of wind on an object. LPFP-core?The force of uniform electric and magnetic fields on an object. LPFP-coreEuler-Cromer method for the  data type. LPFP-coreGiven a numerical method, a list of one-body forces, and an initial state, return a list of states describing how the particle evolves in time. LPFP-coreGiven a numerical method and a list of one-body forces, return a state-update function. LPFP-coreGiven a numerical method, a list of one-body forces, and an initial state, return a position function describing how the particle evolves in time. LPFP-coreGiven a list of forces, return a differential equation based on the theory of special relativity. LPFP-corea differential equation LPFP-coredrag coefficient LPFP-core air density LPFP-corecross-sectional area of object LPFP-core wind velocity LPFP-coredrag coefficient LPFP-core air density LPFP-corecross-sectional area of object LPFP-coreE LPFP-coreB LPFP-corenumerical method LPFP-corelist of force funcs LPFP-coreevolver LPFP-corelist of force funcs LPFP-core initial state LPFP-coreposition function LPFP-coredrag coefficient LPFP-coreair density at sea level LPFP-corecross-sectional area of object::(c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred)g LPFP-core4Force provided by a spring that is fixed at one end.""(c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred*f,,(c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred+  (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred,('' (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred-? (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred.,, (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred/=## (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred0@ (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred1(c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred2))(c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred3(c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Safe-Inferred4n  (c) Scott N. Walck 2023BSD3 (see LICENSE)Scott N. Walck stable Trustworthy5  ! 01234567:;<=>?@ABIJKLMNOPQRSTUVWopqrstuv04321IOPRSVTUWMNQ !JKL=>?@AB56:7 ;?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                                                                                                                    }                                                                 &LPFP-core-1.1.1-FJvUqsgYfJG1lWCW6A3MIsLPFPCore.Newton2LPFPCore.SimpleVecLPFPCore.Mechanics1DLPFPCore.Mechanics3DLPFPCore.MultipleObjectsLPFPCore.MOExamplesLPFPCore.ElectricityLPFPCore.CoordinateSystemsLPFPCore.LorentzLPFPCore.GeometryLPFPCore.IntegralsLPFPCore.ChargeLPFPCore.ElectricFieldLPFPCore.MaxwellLPFPCore.CurrentLPFPCore.MagneticFieldLPFPCoreForceVelocityPositionTimeMassR velocityCF positionCF velocityFtantiDerivativeintegral positionFt pedalCoastfAir newtonSecondVupdateVelocity velocityFv bikeVelocitynewtonSecondTVupdateTVstatesTV velocityFtv pedalCoastAirpedalCoastAir2 velocityCF'sumF positionFv positionFtv updateExampleVecxCompyCompzCompMyMaybe MyNothingMyJustMyBoolMyFalseMyTrue GradeRecordnamegradeGrade AccelerationPosVec Derivative VecDerivative vecDerivativev1 xCompFunc derivative velFromPos accFromVel positionCV velocityCA positionCA aParallelaPerpspeedRateChangeradiusOfCurvature projectilePosgrades gradeRecords1 gradeRecords2 showDoubleveciHatjHatkHatzeroVnegateV^+^^-^sumV*^^*<.>><^/ magnitude vecIntegral maxHeightspeedCAxyProj magAnglesgEarthvBallspeedRateChangeBallrNCMaPerpFromPosition $fShowVec$fEqVec $fEqMyMaybe $fShowMyMaybe $fEqMyBool $fShowMyBool$fEqGradeRecord$fShowGradeRecord $fEqGrade $fShowGrade$fEqMass $fShowMassMStateDiffshiftRealVectorSpace+++scaleNumericalMethodDifferentialEquationUpdateFunctionState1DTimeStepnewtonSecond1Deuler1D updateTXV statesTXV velocity1D velocityFtxv position1D positionFtxv springForcedampedHOForcesdampedHOStatespingpongPositionpingpongVelocity eulerCromer1D updateTXVECsolvereuler rungeKutta4 exponentialupdate2 earthGravity earthGravity2 positionFtxv2 statesTXV2 updateTXV2 updateTV'forcesvdp$fRealVectorSpace(,)$fRealVectorSpace(,,) $fDiff(,)(,)$fDiff(,,)(,,)HasTimetimeOfDParticleStatedmdtdqdtdtdtdrdtdvdt OneBodyForce ParticleStatemasschargetimeposVecvelocitydefaultParticleState rockStatenewtonSecondPSearthSurfaceGravity sunGravity airResistance windForceuniformLorentzForce eulerCromerPSstatesPSupdatePS positionPS constantForcemoonSurfaceGravitytvyPairtvyPairstle1yr stateFuncairResAtAltitudeprojectileRangeComparison halleyUpdate halleyInitialbaseballForcesbaseballTrajectoryzGE0 trajectory baseballRange bestAngleprojectileUpdateprojectileInitial protonUpdate protonInitialapR wallForceenergy firstOrbit relativityPS twoProtUpdatetwoProtInitial relativityPS'!$fDiffParticleStateDParticleState$fRealVectorSpaceDParticleState$fHasTimeParticleState$fShowDParticleState$fShowParticleStateDMultiParticleStateDMPSMultiParticleStateMPSparticleStates ExternalForce InternalForce ForceVector TwoBodyForce oneFromTwogravityMagnitudeuniversalGravityconstantRepulsiveForceWrongconstantRepulsiveForce linearSpringfixedLinearSpring centralForcelinearSpringCentral billiardForcenewtonSecondMPSforcesOnforceOneulerCromerMPS updateMPS statesMPSspeeduniversalGravity'universalGravityCentral lennardJonessystemKE forcesOn'externalForcesOninternalForcesOn$fHasTimeMultiParticleState+$fDiffMultiParticleStateDMultiParticleState$$fRealVectorSpaceDMultiParticleState$fShowDMultiParticleState$fShowMultiParticleStateTable JustificationLJRJtwoSpringsForcestwoSpringsInitialtwoSpringsUpdate kineticEnergylinearSpringPEearthSurfaceGravityPE twoSpringsPE twoSpringsMEbilliardForces ballRadiusbilliardDiffEqbilliardUpdatebilliardEvolverbilliardInitialbilliardStatesbilliardStatesFinitemomentumsystemPpercentChangePMagsigFigspTablepTableEupercentChangeKEtenthskeTable contactSteps inContact contactTableclosest separation closestTable forcesString stringUpdatestringInitialOvertonestringInitialPluckmpsPosmpsVel dissipation $fShowTable$fShowJustificationChargeelementaryChargecoulombMagnitude coulombForcetwoProtonStatesinitialTwoProtonStateoneProtonVelocitytvPairsoneProtonPosition VectorField ScalarField DisplacementCoordinateSystemCart cartesian cylindrical sphericalcartcylsphorigincartesianCoordinatescylindricalCoordinatessphericalCoordinates displacement shiftPositionxSFrSFfst3snd3thd3ySFsHatphiHatrHatthetaHatxHatyHatzHatrVFaddScalarFieldsaddVectorFieldssfTablemagRadthetaSF thetaHat3D phiHatGrad$fShowPositionDParticleFieldStatedEdtdBdtParticleFieldStateposition electricField magneticField lorentzForcenewtonSecondPFS pfsUpdate defaultPFSscalePosnewtonSecondPFS'$fHasTimeParticleFieldState+$fDiffParticleFieldStateDParticleFieldState$$fRealVectorSpaceDParticleFieldStateVolume volumeFuncloLimitupLimitloCurveupCurveloSurfupSurfSurface surfaceFunc lowerLimit upperLimit lowerCurve upperCurveCurve curveFuncstartingCurveParamendingCurveParamcircle2circle2' unitCircle straightLine unitSphere unitSphere'parabolaSurface shiftSurfacecenteredSpherespherenorthernHemispherediskunitConeunitBallcenteredCylindercirclesquare squareFuncnorthernHalfBall centeredBall shiftVolumequarterDiskBoundaryquarterCylinder ParamCubePCv000v001v010v011v100v101v110v111TetTriangleTriSegment VolumeApprox SurfaceApprox CurveApproxscalarLineIntegralscalarSurfaceIntegralscalarVolumeIntegralvectorLineIntegralvectorSurfaceIntegralvectorVolumeIntegral curveSamplesegments linSpaced surfaceSample triCentertriArea triangles volumeSample tetCenter tetVolume tetrahedronsChargeDistribution PointCharge LineCharge SurfaceCharge VolumeChargeMultipleCharges protonOrigin chargedLine chargedBalldiskCap totalCharge simpleDipoleelectricDipoleMoment lineDipole chargedDiskcircularLineChargechargedSquarePlatechargedSphericalShell chargedCube squareCaphydrogenAbstractVector zeroVectoraddFieldScalarVolumeIntegralScalarSurfaceIntegralScalarLineIntegralVectorVolumeIntegralVectorSurfaceIntegralVectorLineIntegralepsilon0cSImu0eFieldFromPointChargeeFieldsimpleDipoleSodiumChlorideeFieldSodiumChlorideeFieldIdealDipoleeFieldFromLineChargelineDipoleSodiumChlorideeFieldLineDipoleeFieldFromSurfaceCharge eFieldDiskCapeFieldFromVolumeChargesumGgeneralLineIntegraldottedSurfaceIntegralelectricFluxFromFieldelectricFluxFromChargeeFieldFromSurfaceChargeP surfaceAreadottedLineIntegralelectricPotentialFromField StateFDTDtimeFDTDstepXstepYstepZbField FieldStatedirectionalDerivativecurl maxwellUpdate maxwellEvolveexLocseyLocsezLocsbxLocsbyLocsbzLocs spaceStepsCEhiEvenevensoddsinitialStateFDTDlookupAZpartialXpartialYpartialZcurlBxcurlBycurlBzcurlExcurlEycurlEz stateUpdateupdateEupdateB updateEOneLoc updateBOneLoc jGaussian getAverage$fShowStateFDTDCurrentDistribution LineCurrentSurfaceCurrent VolumeCurrentMultipleCurrentsCurrentcircularCurrentLoop wireSolenoid sheetSolenoid wireToroidcrossedLineIntegralmagneticDipoleMoment helmholtzCoillongStraightWiretorus totalCurrentbFieldFromLineCurrentcircleBbFieldIdealDipolebFieldWireToroidbFieldFromSurfaceCurrentbFieldFromVolumeCurrentmagneticFluxFromFieldmagneticFluxFromCurrentvisLoop