Copyright	(c) Scott N. Walck 2023
License	BSD3 (see LICENSE)
Maintainer	Scott N. Walck <walck@lvc.edu>
Stability	stable
Safe Haskell	Trustworthy
Language	Haskell2010

LPFPCore

Contents

(Approximations to) Real numbers
Vectors
Calculus
- Differential equations
3D Mechanics
- Single particle state
- One-body forces
Interacting particles
- Two-body forces
Electricity
Coordinate Systems
Geometry
Electromagnetic Theory

Description

Code from the book Learn Physics with Functional Programming

Synopsis

type R = Double
type Time = R
data Vec
type PosVec = Vec
type Velocity = Vec
type Acceleration = Vec
vec :: R -> R -> R -> Vec
(^+^) :: Vec -> Vec -> Vec
(^-^) :: Vec -> Vec -> Vec
(*^) :: R -> Vec -> Vec
(^*) :: Vec -> R -> Vec
(^/) :: Vec -> R -> Vec
(<.>) :: Vec -> Vec -> R
(><) :: Vec -> Vec -> Vec
magnitude :: Vec -> R
zeroV :: Vec
negateV :: Vec -> Vec
sumV :: [Vec] -> Vec
xComp :: Vec -> R
yComp :: Vec -> R
zComp :: Vec -> R
iHat :: Vec
jHat :: Vec
kHat :: Vec
positionCV :: PosVec -> Velocity -> Time -> PosVec
velocityCA :: Velocity -> Acceleration -> Time -> Velocity
positionCA :: PosVec -> Velocity -> Acceleration -> Time -> PosVec
aParallel :: Vec -> Vec -> Vec
aPerp :: Vec -> Vec -> Vec
speedRateChange :: Vec -> Vec -> R
type Derivative = (R -> R) -> R -> R
type VecDerivative = (R -> Vec) -> R -> Vec
derivative :: R -> Derivative
vecDerivative :: R -> VecDerivative
integral :: R -> (R -> R) -> R -> R -> R
antiDerivative :: R -> R -> (R -> R) -> R -> R
velFromPos :: R -> (Time -> PosVec) -> Time -> Velocity
accFromVel :: R -> (Time -> Velocity) -> Time -> Acceleration
type UpdateFunction s = s -> s
type DifferentialEquation s ds = s -> ds
type NumericalMethod s ds = DifferentialEquation s ds -> UpdateFunction s
class RealVectorSpace ds where
- (+++) :: ds -> ds -> ds
- scale :: R -> ds -> ds
class RealVectorSpace ds => Diff s ds where
- shift :: R -> ds -> s -> s
solver :: NumericalMethod s ds -> DifferentialEquation s ds -> s -> [s]
euler :: Diff s ds => R -> (s -> ds) -> s -> s
rungeKutta4 :: Diff s ds => R -> (s -> ds) -> s -> s
data ParticleState = ParticleState {
- mass :: R
- charge :: R
- time :: R
- posVec :: Vec
- velocity :: Vec
}
data DParticleState = DParticleState {
- dmdt :: R
- dqdt :: R
- dtdt :: R
- drdt :: Vec
- dvdt :: Vec
}
class HasTime s where
- timeOf :: s -> Time
defaultParticleState :: ParticleState
newtonSecondPS :: [OneBodyForce] -> ParticleState -> DParticleState
relativityPS :: [OneBodyForce] -> ParticleState -> DParticleState
eulerCromerPS :: TimeStep -> NumericalMethod ParticleState DParticleState
statesPS :: NumericalMethod ParticleState DParticleState -> [OneBodyForce] -> ParticleState -> [ParticleState]
updatePS :: NumericalMethod ParticleState DParticleState -> [OneBodyForce] -> ParticleState -> ParticleState
type OneBodyForce = ParticleState -> Vec
earthSurfaceGravity :: OneBodyForce
sunGravity :: OneBodyForce
airResistance :: R -> R -> R -> OneBodyForce
windForce :: Vec -> R -> R -> R -> OneBodyForce
uniformLorentzForce :: Vec -> Vec -> OneBodyForce
fixedLinearSpring :: R -> R -> Vec -> OneBodyForce
data Force
- = ExternalForce Int OneBodyForce
- | InternalForce Int Int TwoBodyForce
data MultiParticleState = MPS {
- particleStates :: [ParticleState]
}
data DMultiParticleState = DMPS [DParticleState]
type TwoBodyForce = ParticleState -> ParticleState -> ForceVector
universalGravity :: TwoBodyForce
linearSpring :: R -> R -> TwoBodyForce
centralForce :: (R -> R) -> TwoBodyForce
billiardForce :: R -> R -> TwoBodyForce
newtonSecondMPS :: [Force] -> MultiParticleState -> DMultiParticleState
eulerCromerMPS :: TimeStep -> NumericalMethod MultiParticleState DMultiParticleState
updateMPS :: NumericalMethod MultiParticleState DMultiParticleState -> [Force] -> MultiParticleState -> MultiParticleState
statesMPS :: NumericalMethod MultiParticleState DMultiParticleState -> [Force] -> MultiParticleState -> [MultiParticleState]
data Justification
- = LJ
- | RJ
data Table a = Table Justification [[a]]
kineticEnergy :: ParticleState -> R
systemKE :: MultiParticleState -> R
momentum :: ParticleState -> Vec
systemP :: MultiParticleState -> Vec
linearSpringPE :: R -> R -> ParticleState -> ParticleState -> R
earthSurfaceGravityPE :: ParticleState -> R
tenths :: R -> Float
sigFigs :: Int -> R -> Float
elementaryCharge :: Charge
coulombForce :: TwoBodyForce
data Position
type Displacement = Vec
type ScalarField = Position -> R
type VectorField = Position -> Vec
type CoordinateSystem = (R, R, R) -> Position
cartesian :: CoordinateSystem
cylindrical :: CoordinateSystem
spherical :: CoordinateSystem
cart :: R -> R -> R -> Position
cyl :: R -> R -> R -> Position
sph :: R -> R -> R -> Position
cartesianCoordinates :: Position -> (R, R, R)
cylindricalCoordinates :: Position -> (R, R, R)
sphericalCoordinates :: Position -> (R, R, R)
displacement :: Position -> Position -> Displacement
shiftPosition :: Displacement -> Position -> Position
rHat :: VectorField
thetaHat :: VectorField
phiHat :: VectorField
sHat :: VectorField
xHat :: VectorField
yHat :: VectorField
zHat :: VectorField
origin :: Position
xSF :: ScalarField
ySF :: ScalarField
rSF :: ScalarField
rVF :: VectorField
fst3 :: (a, b, c) -> a
snd3 :: (a, b, c) -> b
thd3 :: (a, b, c) -> c
addScalarFields :: [ScalarField] -> ScalarField
addVectorFields :: [VectorField] -> VectorField
sfTable :: ((R, R) -> Position) -> [R] -> [R] -> ScalarField -> Table Int
data Curve = Curve {
- curveFunc :: R -> Position
- startingCurveParam :: R
- endingCurveParam :: R
}
unitCircle :: Curve
straightLine :: Position -> Position -> Curve
data Surface = Surface {
- surfaceFunc :: (R, R) -> Position
- lowerLimit :: R
- upperLimit :: R
- lowerCurve :: R -> R
- upperCurve :: R -> R
}
unitSphere :: Surface
centeredSphere :: R -> Surface
sphere :: R -> Position -> Surface
northernHemisphere :: Surface
disk :: R -> Surface
shiftSurface :: Vec -> Surface -> Surface
data Volume = Volume {
- volumeFunc :: (R, R, R) -> Position
- loLimit :: R
- upLimit :: R
- loCurve :: R -> R
- upCurve :: R -> R
- loSurf :: R -> R -> R
- upSurf :: R -> R -> R
}
unitBall :: Volume
centeredBall :: R -> Volume
northernHalfBall :: Volume
centeredCylinder :: R -> R -> Volume
type Charge = R
data ChargeDistribution
- = PointCharge Charge Position
- | LineCharge ScalarField Curve
- | SurfaceCharge ScalarField Surface
- | VolumeCharge ScalarField Volume
- | MultipleCharges [ChargeDistribution]
totalCharge :: ChargeDistribution -> Charge
electricDipoleMoment :: ChargeDistribution -> Vec
epsilon0 :: R
cSI :: R
mu0 :: R
eField :: ChargeDistribution -> VectorField
type ScalarLineIntegral = ScalarField -> Curve -> R
type ScalarSurfaceIntegral = ScalarField -> Surface -> R
type ScalarVolumeIntegral = ScalarField -> Volume -> R
type VectorLineIntegral = VectorField -> Curve -> Vec
type VectorSurfaceIntegral = VectorField -> Surface -> Vec
type VectorVolumeIntegral = VectorField -> Volume -> Vec
type CurveApprox = Curve -> [(Position, Vec)]
type SurfaceApprox = Surface -> [(Position, Vec)]
type VolumeApprox = Volume -> [(Position, R)]
scalarLineIntegral :: CurveApprox -> ScalarField -> Curve -> R
scalarSurfaceIntegral :: SurfaceApprox -> ScalarField -> Surface -> R
scalarVolumeIntegral :: VolumeApprox -> ScalarField -> Volume -> R
vectorLineIntegral :: CurveApprox -> VectorField -> Curve -> Vec
vectorSurfaceIntegral :: SurfaceApprox -> VectorField -> Surface -> Vec
vectorVolumeIntegral :: VolumeApprox -> VectorField -> Volume -> Vec
dottedLineIntegral :: CurveApprox -> VectorField -> Curve -> R
dottedSurfaceIntegral :: SurfaceApprox -> VectorField -> Surface -> R
curveSample :: Int -> Curve -> [(Position, Vec)]
surfaceSample :: Int -> Surface -> [(Position, Vec)]
volumeSample :: Int -> Volume -> [(Position, R)]
type Field a = Position -> a
type Current = R
data CurrentDistribution
- = LineCurrent Current Curve
- | SurfaceCurrent VectorField Surface
- | VolumeCurrent VectorField Volume
- | MultipleCurrents [CurrentDistribution]
crossedLineIntegral :: CurveApprox -> VectorField -> Curve -> Vec
totalCurrent :: VectorField -> Surface -> Current
magneticDipoleMoment :: CurrentDistribution -> Vec
bField :: CurrentDistribution -> VectorField
lorentzForce :: ParticleFieldState -> Vec
newtonSecondPFS :: ParticleFieldState -> DParticleFieldState
defaultPFS :: ParticleFieldState
directionalDerivative :: Vec -> ScalarField -> ScalarField
curl :: R -> VectorField -> VectorField
type FieldState = (R, VectorField, VectorField)

(Approximations to) Real numbers

type R = Double Source #

An approximation to a real number.

type Time = R Source #

Time is a real number.

Vectors

data Vec Source #

A type for three-dimensional vectors.

Instances

Instances details

Show Vec Source #
Instance details Defined in LPFPCore.SimpleVec Methods showsPrec :: Int -> Vec -> ShowS # show :: Vec -> String # showList :: [Vec] -> ShowS #
Eq Vec Source #
Instance details Defined in LPFPCore.SimpleVec Methods (==) :: Vec -> Vec -> Bool # (/=) :: Vec -> Vec -> Bool #

type PosVec = Vec Source #

The position of a particle can be represented as a vector.

type Velocity = Vec Source #

Velocity is a vector.

type Acceleration = Vec Source #

Acceleration is a vector.

vec Source #

Arguments

:: R	x component
-> R	y component
-> R	z component
-> Vec

Form a vector by giving its x, y, and z components.

(^+^) :: Vec -> Vec -> Vec infixl 6 Source #

Vector addition.

(^-^) :: Vec -> Vec -> Vec infixl 6 Source #

Vector subtraction.

(*^) :: R -> Vec -> Vec infixr 7 Source #

Scalar multiplication of a number and a vector.

(^*) :: Vec -> R -> Vec infixl 7 Source #

Scalar multiplication of a vector and a number.

(^/) :: Vec -> R -> Vec infixr 7 Source #

Division of a vector by a number.

(<.>) :: Vec -> Vec -> R infixr 7 Source #

Dot product of two vectors.

(><) :: Vec -> Vec -> Vec infixl 7 Source #

Cross product of two vectors.

magnitude :: Vec -> R Source #

Magnitude of a vector.

zeroV :: Vec Source #

The zero vector.

negateV :: Vec -> Vec Source #

Negate a vector.

sumV :: [Vec] -> Vec Source #

Add a list of vectors.

xComp :: Vec -> R Source #

x component of a vector

yComp :: Vec -> R Source #

y component of a vector

zComp :: Vec -> R Source #

z component of a vector

iHat :: Vec Source #

A unit vector in the x direction.

jHat :: Vec Source #

A unit vector in the y direction.

kHat :: Vec Source #

A unit vector in the z direction.

positionCV :: PosVec -> Velocity -> Time -> PosVec Source #

Given initial position and a constant velocity, return a position function.

velocityCA :: Velocity -> Acceleration -> Time -> Velocity Source #

Given initial velocity and a constant acceleration, return a velocity function.

positionCA :: PosVec -> Velocity -> Acceleration -> Time -> PosVec Source #

Given initial position, initial velocity, and a constant acceleration, return a position function.

aParallel :: Vec -> Vec -> Vec Source #

Given a nonzero velocity and an acceleration, return the component of acceleration parallel to the velocity.

aPerp :: Vec -> Vec -> Vec Source #

Given a nonzero velocity and an acceleration, return the component of acceleration perpendicular to the velocity.

speedRateChange :: Vec -> Vec -> R Source #

Given velocity and acceleration, return the rate at which speed is changing.

Calculus

type Derivative = (R -> R) -> R -> R Source #

A 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.

type VecDerivative = (R -> Vec) -> R -> Vec Source #

A 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.

derivative :: R -> Derivative Source #

Given a step size, calculate the derivative of a real-valued function of a real variable (often time).

vecDerivative :: R -> VecDerivative Source #

Given a step size, calculate the vector derivative of a vector-valued function of a real variable (usually time).

integral :: R -> (R -> R) -> R -> R -> R Source #

Given a step size, a function, a lower limit, and an upper limit, return the definite integral of the function.

antiDerivative :: R -> R -> (R -> R) -> R -> R Source #

Given a step size, a y-intercept, and a function, return a function with the given y-intercept whose derivative is the given function.

velFromPos Source #

Arguments

:: R	dt
-> (Time -> PosVec)	position function
-> Time -> Velocity	velocity function

Given a time step and a position function, return a velocity function.

accFromVel :: R -> (Time -> Velocity) -> Time -> Acceleration Source #

Given a time step and a velocity function, return an acceleration function.

Differential equations

type UpdateFunction s = s -> s Source #

An update function takes a state as input and returns an updated state as output.

type DifferentialEquation s ds = s -> ds Source #

A differential equation takes a state as input and returns as output the rate at which the state is changing.

type NumericalMethod s ds = DifferentialEquation s ds -> UpdateFunction s Source #

A numerical method turns a differential equation into a state-update function.

class RealVectorSpace ds where Source #

A real vector space allows vector addition and scalar multiplication by reals.

Methods

(+++) :: ds -> ds -> ds Source #

scale :: R -> ds -> ds Source #

Instances

Instances details

RealVectorSpace DParticleFieldState Source #
Instance details Defined in LPFPCore.Lorentz Methods (+++) :: DParticleFieldState -> DParticleFieldState -> DParticleFieldState Source # scale :: R -> DParticleFieldState -> DParticleFieldState Source #
RealVectorSpace DParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods (+++) :: DParticleState -> DParticleState -> DParticleState Source # scale :: R -> DParticleState -> DParticleState Source #
RealVectorSpace DMultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods (+++) :: DMultiParticleState -> DMultiParticleState -> DMultiParticleState Source # scale :: R -> DMultiParticleState -> DMultiParticleState Source #
RealVectorSpace (R, R) Source #
Instance details Defined in LPFPCore.Mechanics1D Methods (+++) :: (R, R) -> (R, R) -> (R, R) Source # scale :: R -> (R, R) -> (R, R) Source #
RealVectorSpace (R, R, R) Source #	A triple of real numbers is a real vector space.
Instance details Defined in LPFPCore.Mechanics1D Methods (+++) :: (R, R, R) -> (R, R, R) -> (R, R, R) Source # scale :: R -> (R, R, R) -> (R, R, R) Source #

class RealVectorSpace ds => Diff s ds where Source #

A type class that expresses a relationship between a state space and a time-derivative-state space.

Methods

shift :: R -> ds -> s -> s Source #

Instances

Instances details

Diff ParticleFieldState DParticleFieldState Source #
Instance details Defined in LPFPCore.Lorentz Methods shift :: R -> DParticleFieldState -> ParticleFieldState -> ParticleFieldState Source #
Diff ParticleState DParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods shift :: R -> DParticleState -> ParticleState -> ParticleState Source #
Diff MultiParticleState DMultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods shift :: R -> DMultiParticleState -> MultiParticleState -> MultiParticleState Source #
Diff State1D (R, R, R) Source #	A triple of real numbers can serve as the time derivative of a `State1D`.
Instance details Defined in LPFPCore.Mechanics1D Methods shift :: R -> (R, R, R) -> State1D -> State1D Source #
Diff (Time, Velocity) (R, R) Source #
Instance details Defined in LPFPCore.Mechanics1D Methods shift :: R -> (R, R) -> (Time, Velocity) -> (Time, Velocity) Source #

solver :: NumericalMethod s ds -> DifferentialEquation s ds -> s -> [s] Source #

Given a numerical method, a differential equation, and an initial state, return a list of states.

euler :: Diff s ds => R -> (s -> ds) -> s -> s Source #

Given a step size, return the numerical method that uses the Euler method with that step size.

rungeKutta4 :: Diff s ds => R -> (s -> ds) -> s -> s Source #

Given a step size, return the numerical method that uses the 4th order Runge Kutta method with that step size.

3D Mechanics

Single particle state

data ParticleState Source #

Data type for the state of a single particle in three-dimensional space.

Constructors

ParticleState
Fields mass :: R charge :: R time :: R posVec :: Vec velocity :: Vec

Instances

Instances details

HasTime ParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods timeOf :: ParticleState -> Time Source #
Show ParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods showsPrec :: Int -> ParticleState -> ShowS # show :: ParticleState -> String # showList :: [ParticleState] -> ShowS #
Diff ParticleState DParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods shift :: R -> DParticleState -> ParticleState -> ParticleState Source #

data DParticleState Source #

Data type for the time-derivative of a particle state.

Constructors

DParticleState
Fields dmdt :: R dqdt :: R dtdt :: R drdt :: Vec dvdt :: Vec

Instances

Instances details

RealVectorSpace DParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods (+++) :: DParticleState -> DParticleState -> DParticleState Source # scale :: R -> DParticleState -> DParticleState Source #
Show DParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods showsPrec :: Int -> DParticleState -> ShowS # show :: DParticleState -> String # showList :: [DParticleState] -> ShowS #
Diff ParticleState DParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods shift :: R -> DParticleState -> ParticleState -> ParticleState Source #

class HasTime s where Source #

Methods

timeOf :: s -> Time Source #

Instances

Instances details

HasTime ParticleFieldState Source #
Instance details Defined in LPFPCore.Lorentz Methods timeOf :: ParticleFieldState -> Time Source #
HasTime ParticleState Source #
Instance details Defined in LPFPCore.Mechanics3D Methods timeOf :: ParticleState -> Time Source #
HasTime MultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods timeOf :: MultiParticleState -> Time Source #

defaultParticleState :: ParticleState Source #

A default particle state.

newtonSecondPS Source #

Arguments

:: [OneBodyForce]
-> ParticleState
-> DParticleState	a differential equation

Given a list of forces, return a differential equation based on Newton's second law.

relativityPS :: [OneBodyForce] -> ParticleState -> DParticleState Source #

Given a list of forces, return a differential equation based on the theory of special relativity.

eulerCromerPS :: TimeStep -> NumericalMethod ParticleState DParticleState Source #

Euler-Cromer method for the ParticleState data type.

statesPS Source #

Arguments

:: NumericalMethod ParticleState DParticleState	numerical method
-> [OneBodyForce]	list of force funcs
-> ParticleState
-> [ParticleState]	evolver

Given 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.

updatePS :: NumericalMethod ParticleState DParticleState -> [OneBodyForce] -> ParticleState -> ParticleState Source #

Given a numerical method and a list of one-body forces, return a state-update function.

One-body forces

type OneBodyForce = ParticleState -> Vec Source #

Data type for a one-body force.

earthSurfaceGravity :: OneBodyForce Source #

The force of gravity near Earth's surface. The z direction is toward the sky. Assumes SI units.

sunGravity :: OneBodyForce Source #

The force of the Sun's gravity on an object. The origin is at center of the Sun. Assumes SI units.

airResistance Source #

Arguments

:: R	drag coefficient
-> R	air density
-> R	cross-sectional area of object
-> OneBodyForce

The force of air resistance on an object.

windForce Source #

Arguments

:: Vec	wind velocity
-> R	drag coefficient
-> R	air density
-> R	cross-sectional area of object
-> OneBodyForce

The force of wind on an object.

uniformLorentzForce Source #

Arguments

:: Vec	E
-> Vec	B
-> OneBodyForce

The force of uniform electric and magnetic fields on an object.

fixedLinearSpring :: R -> R -> Vec -> OneBodyForce Source #

Force provided by a spring that is fixed at one end.

Interacting particles

data Force Source #

Constructors

ExternalForce Int OneBodyForce
InternalForce Int Int TwoBodyForce

data MultiParticleState Source #

Constructors

MPS
Fields particleStates :: [ParticleState]

Instances

Instances details

HasTime MultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods timeOf :: MultiParticleState -> Time Source #
Show MultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods showsPrec :: Int -> MultiParticleState -> ShowS # show :: MultiParticleState -> String # showList :: [MultiParticleState] -> ShowS #
Diff MultiParticleState DMultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods shift :: R -> DMultiParticleState -> MultiParticleState -> MultiParticleState Source #

data DMultiParticleState Source #

Constructors

DMPS [DParticleState]

Instances

Instances details

RealVectorSpace DMultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods (+++) :: DMultiParticleState -> DMultiParticleState -> DMultiParticleState Source # scale :: R -> DMultiParticleState -> DMultiParticleState Source #
Show DMultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods showsPrec :: Int -> DMultiParticleState -> ShowS # show :: DMultiParticleState -> String # showList :: [DMultiParticleState] -> ShowS #
Diff MultiParticleState DMultiParticleState Source #
Instance details Defined in LPFPCore.MultipleObjects Methods shift :: R -> DMultiParticleState -> MultiParticleState -> MultiParticleState Source #

Two-body forces

type TwoBodyForce = ParticleState -> ParticleState -> ForceVector Source #

universalGravity :: TwoBodyForce Source #

linearSpring :: R -> R -> TwoBodyForce Source #

centralForce :: (R -> R) -> TwoBodyForce Source #

billiardForce :: R -> R -> TwoBodyForce Source #

newtonSecondMPS :: [Force] -> MultiParticleState -> DMultiParticleState Source #

eulerCromerMPS :: TimeStep -> NumericalMethod MultiParticleState DMultiParticleState Source #

updateMPS :: NumericalMethod MultiParticleState DMultiParticleState -> [Force] -> MultiParticleState -> MultiParticleState Source #

statesMPS :: NumericalMethod MultiParticleState DMultiParticleState -> [Force] -> MultiParticleState -> [MultiParticleState] Source #

data Justification Source #

Constructors

LJ
RJ

Instances

Instances details

Show Justification Source #
Instance details Defined in LPFPCore.MOExamples Methods showsPrec :: Int -> Justification -> ShowS # show :: Justification -> String # showList :: [Justification] -> ShowS #

data Table a Source #

Constructors

Table Justification [[a]]

Instances

Instances details

Show a => Show (Table a) Source #
Instance details Defined in LPFPCore.MOExamples Methods showsPrec :: Int -> Table a -> ShowS # show :: Table a -> String # showList :: [Table a] -> ShowS #

kineticEnergy :: ParticleState -> R Source #

systemKE :: MultiParticleState -> R Source #

momentum :: ParticleState -> Vec Source #

systemP :: MultiParticleState -> Vec Source #

linearSpringPE :: R -> R -> ParticleState -> ParticleState -> R Source #

earthSurfaceGravityPE :: ParticleState -> R Source #

tenths :: R -> Float Source #

sigFigs :: Int -> R -> Float Source #

Electricity

elementaryCharge :: Charge Source #

coulombForce :: TwoBodyForce Source #

Coordinate Systems

data Position Source #

Instances

Instances details

Show Position Source #
Instance details Defined in LPFPCore.CoordinateSystems Methods showsPrec :: Int -> Position -> ShowS # show :: Position -> String # showList :: [Position] -> ShowS #

type Displacement = Vec Source #

type ScalarField = Position -> R Source #

type VectorField = Position -> Vec Source #

type CoordinateSystem = (R, R, R) -> Position Source #

cartesian :: CoordinateSystem Source #

cylindrical :: CoordinateSystem Source #

spherical :: CoordinateSystem Source #

cart :: R -> R -> R -> Position Source #

cyl :: R -> R -> R -> Position Source #

sph :: R -> R -> R -> Position Source #

cartesianCoordinates :: Position -> (R, R, R) Source #

cylindricalCoordinates :: Position -> (R, R, R) Source #

sphericalCoordinates :: Position -> (R, R, R) Source #

displacement :: Position -> Position -> Displacement Source #

shiftPosition :: Displacement -> Position -> Position Source #

rHat :: VectorField Source #

thetaHat :: VectorField Source #

phiHat :: VectorField Source #

sHat :: VectorField Source #

xHat :: VectorField Source #

yHat :: VectorField Source #

zHat :: VectorField Source #

origin :: Position Source #

xSF :: ScalarField Source #

ySF :: ScalarField Source #

rSF :: ScalarField Source #

rVF :: VectorField Source #

fst3 :: (a, b, c) -> a Source #

snd3 :: (a, b, c) -> b Source #

thd3 :: (a, b, c) -> c Source #

addScalarFields :: [ScalarField] -> ScalarField Source #

addVectorFields :: [VectorField] -> VectorField Source #

sfTable :: ((R, R) -> Position) -> [R] -> [R] -> ScalarField -> Table Int Source #

Geometry

data Curve Source #

Constructors

Curve
Fields curveFunc :: R -> Position startingCurveParam :: R endingCurveParam :: R

unitCircle :: Curve Source #

straightLine :: Position -> Position -> Curve Source #

data Surface Source #

Constructors

Surface
Fields surfaceFunc :: (R, R) -> Position lowerLimit :: R upperLimit :: R lowerCurve :: R -> R upperCurve :: R -> R

unitSphere :: Surface Source #

centeredSphere :: R -> Surface Source #

sphere :: R -> Position -> Surface Source #

northernHemisphere :: Surface Source #

disk :: R -> Surface Source #

shiftSurface :: Vec -> Surface -> Surface Source #

data Volume Source #

Constructors

Volume
Fields volumeFunc :: (R, R, R) -> Position loLimit :: R upLimit :: R loCurve :: R -> R upCurve :: R -> R loSurf :: R -> R -> R upSurf :: R -> R -> R

unitBall :: Volume Source #

centeredBall :: R -> Volume Source #

northernHalfBall :: Volume Source #

centeredCylinder :: R -> R -> Volume Source #

Electromagnetic Theory

Charge

type Charge = R Source #

data ChargeDistribution Source #

Constructors

PointCharge Charge Position
LineCharge ScalarField Curve
SurfaceCharge ScalarField Surface
VolumeCharge ScalarField Volume
MultipleCharges [ChargeDistribution]