LPFPCore.SimpleVec

Code from chapter 10 of the book Learn Physics with Functional Programming

Documentation

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

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.

vecDerivative :: R -> VecDerivative

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

v1 :: R -> Vec

xCompFunc :: (R -> Vec) -> R -> R

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

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.

derivative :: R -> Derivative

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

type Time = R

Time is a real number.

type PosVec = Vec

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

type Velocity = Vec

Velocity is a vector.

type Acceleration = Vec

Acceleration is a vector.

velFromPos

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

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

positionCV :: PosVec -> Velocity -> Time -> PosVec

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

velocityCA :: Velocity -> Acceleration -> Time -> Velocity

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

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

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

aParallel :: Vec -> Vec -> Vec

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

aPerp :: Vec -> Vec -> Vec

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

speedRateChange :: Vec -> Vec -> R

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

radiusOfCurvature :: Vec -> Vec -> R

projectilePos :: PosVec -> Velocity -> Time -> PosVec

type R = Double

An approximation to a real number.

data Mass

Constructors

Mass R

Instances

Show Mass

Defined in LPFPCore.SimpleVec

Methods

showsPrec :: Int -> Mass -> ShowS

show :: Mass -> String

showList :: [Mass] -> ShowS

Eq Mass

Defined in LPFPCore.SimpleVec

Methods

(==) :: Mass -> Mass -> Bool

(/=) :: Mass -> Mass -> Bool

data Grade

Constructors

Grade String Int

Instances

Show Grade

Defined in LPFPCore.SimpleVec

Methods

showsPrec :: Int -> Grade -> ShowS

show :: Grade -> String

showList :: [Grade] -> ShowS

Eq Grade

Defined in LPFPCore.SimpleVec

Methods

(==) :: Grade -> Grade -> Bool

(/=) :: Grade -> Grade -> Bool

grades :: [Grade]

data GradeRecord

Constructors

GradeRecord

Fields

• name :: String
• grade :: Int

Instances

Show GradeRecord

Defined in LPFPCore.SimpleVec

Methods

showsPrec :: Int -> GradeRecord -> ShowS

show :: GradeRecord -> String

showList :: [GradeRecord] -> ShowS

Eq GradeRecord

Defined in LPFPCore.SimpleVec

Methods

(==) :: GradeRecord -> GradeRecord -> Bool

(/=) :: GradeRecord -> GradeRecord -> Bool

gradeRecords1 :: [GradeRecord]

gradeRecords2 :: [GradeRecord]

data MyBool

Constructors

MyFalse

MyTrue

Instances

Show MyBool

Defined in LPFPCore.SimpleVec

Methods

showsPrec :: Int -> MyBool -> ShowS

show :: MyBool -> String

showList :: [MyBool] -> ShowS

Eq MyBool

Defined in LPFPCore.SimpleVec

Methods

(==) :: MyBool -> MyBool -> Bool

(/=) :: MyBool -> MyBool -> Bool

data MyMaybe a

Constructors

MyNothing

MyJust a

Instances

Show a => Show (MyMaybe a)

Defined in LPFPCore.SimpleVec

Methods

showsPrec :: Int -> MyMaybe a -> ShowS

show :: MyMaybe a -> String

showList :: [MyMaybe a] -> ShowS

Eq a => Eq (MyMaybe a)

Defined in LPFPCore.SimpleVec

Methods

(==) :: MyMaybe a -> MyMaybe a -> Bool

(/=) :: MyMaybe a -> MyMaybe a -> Bool

data Vec

A type for three-dimensional vectors.

Constructors

Vec

Fields

• xComp :: R

  x component of a vector

• yComp :: R

  y component of a vector

• zComp :: R

  z component of a vector

Instances

Show Vec

Defined in LPFPCore.SimpleVec

Methods

showsPrec :: Int -> Vec -> ShowS

show :: Vec -> String

showList :: [Vec] -> ShowS

Eq Vec

Defined in LPFPCore.SimpleVec

Methods

(==) :: Vec -> Vec -> Bool

(/=) :: Vec -> Vec -> Bool

showDouble :: R -> String

vec

Arguments

:: R

x component

-> R

y component

-> R

z component

-> Vec

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

iHat :: Vec

A unit vector in the x direction.

jHat :: Vec

A unit vector in the y direction.

kHat :: Vec

A unit vector in the z direction.

zeroV :: Vec

The zero vector.

negateV :: Vec -> Vec

Negate a vector.

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

Vector addition.

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

Vector subtraction.

sumV :: [Vec] -> Vec

Add a list of vectors.

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

Scalar multiplication of a number and a vector.

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

Scalar multiplication of a vector and a number.

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

Dot product of two vectors.

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

Cross product of two vectors.

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

Division of a vector by a number.

magnitude :: Vec -> R

Magnitude of a vector.

vecIntegral

Arguments

:: R

step size dt

-> (R -> Vec)

vector-valued function

-> R

lower limit

-> R

upper limit

-> Vec

result

Definite integral of a vector-valued function of a real number.

maxHeight :: PosVec -> Velocity -> R

speedCA :: Velocity -> Acceleration -> Time -> R

xyProj :: Vec -> Vec

magAngles :: Vec -> (R, R, R)

gEarth :: Vec

vBall :: R -> Vec

speedRateChangeBall :: R -> R

rNCM :: (R, R -> R) -> R -> Vec

aPerpFromPosition :: R -> (R -> Vec) -> R -> Vec