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

LPFPCore.Newton2

Description

Code from chapter 14 of the book Learn Physics with Functional Programming

Synopsis

velocityCF :: Mass -> Velocity -> [Force] -> Time -> Velocity
type R = Double
type Mass = R
type Time = R
type Position = R
type Velocity = R
type Force = R
positionCF :: Mass -> Position -> Velocity -> [Force] -> Time -> Position
velocityFt :: R -> Mass -> Velocity -> [Time -> Force] -> Time -> Velocity
antiDerivative :: R -> R -> (R -> R) -> R -> R
integral :: R -> (R -> R) -> R -> R -> R
positionFt :: R -> Mass -> Position -> Velocity -> [Time -> Force] -> Time -> Position
pedalCoast :: Time -> Force
fAir :: R -> R -> R -> Velocity -> Force
newtonSecondV :: Mass -> [Velocity -> Force] -> Velocity -> R
updateVelocity :: R -> Mass -> [Velocity -> Force] -> Velocity -> Velocity
velocityFv :: R -> Mass -> Velocity -> [Velocity -> Force] -> Time -> Velocity
bikeVelocity :: Time -> Velocity
newtonSecondTV :: Mass -> [(Time, Velocity) -> Force] -> (Time, Velocity) -> (R, R)
updateTV :: R -> Mass -> [(Time, Velocity) -> Force] -> (Time, Velocity) -> (Time, Velocity)
statesTV :: R -> Mass -> (Time, Velocity) -> [(Time, Velocity) -> Force] -> [(Time, Velocity)]
velocityFtv :: R -> Mass -> (Time, Velocity) -> [(Time, Velocity) -> Force] -> Time -> Velocity
pedalCoastAir :: [(Time, Velocity)]
pedalCoastAir2 :: Time -> Velocity
velocityCF' :: Mass -> Velocity -> [Force] -> Time -> Velocity
sumF :: [R -> R] -> R -> R
positionFv :: R -> Mass -> Position -> Velocity -> [Velocity -> Force] -> Time -> Position
positionFtv :: R -> Mass -> Position -> Velocity -> [(Time, Velocity) -> Force] -> Time -> Position
updateExample :: (Time, Velocity) -> (Time, Velocity)

Documentation

velocityCF :: Mass -> Velocity -> [Force] -> Time -> Velocity Source #

type R = Double Source #

type Mass = R Source #

type Time = R Source #

type Position = R Source #

type Velocity = R Source #

type Force = R Source #

positionCF :: Mass -> Position -> Velocity -> [Force] -> Time -> Position Source #

velocityFt :: R -> Mass -> Velocity -> [Time -> Force] -> Time -> Velocity Source #

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.

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.

positionFt :: R -> Mass -> Position -> Velocity -> [Time -> Force] -> Time -> Position Source #

pedalCoast :: Time -> Force Source #

fAir :: R -> R -> R -> Velocity -> Force Source #

newtonSecondV :: Mass -> [Velocity -> Force] -> Velocity -> R Source #

updateVelocity :: R -> Mass -> [Velocity -> Force] -> Velocity -> Velocity Source #

velocityFv :: R -> Mass -> Velocity -> [Velocity -> Force] -> Time -> Velocity Source #

bikeVelocity :: Time -> Velocity Source #

newtonSecondTV :: Mass -> [(Time, Velocity) -> Force] -> (Time, Velocity) -> (R, R) Source #

updateTV :: R -> Mass -> [(Time, Velocity) -> Force] -> (Time, Velocity) -> (Time, Velocity) Source #

statesTV :: R -> Mass -> (Time, Velocity) -> [(Time, Velocity) -> Force] -> [(Time, Velocity)] Source #

velocityFtv :: R -> Mass -> (Time, Velocity) -> [(Time, Velocity) -> Force] -> Time -> Velocity Source #

pedalCoastAir :: [(Time, Velocity)] Source #

pedalCoastAir2 :: Time -> Velocity Source #

velocityCF' :: Mass -> Velocity -> [Force] -> Time -> Velocity Source #

sumF :: [R -> R] -> R -> R Source #

positionFv :: R -> Mass -> Position -> Velocity -> [Velocity -> Force] -> Time -> Position Source #

positionFtv :: R -> Mass -> Position -> Velocity -> [(Time, Velocity) -> Force] -> Time -> Position Source #

updateExample :: (Time, Velocity) -> (Time, Velocity) Source #