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.Mechanics1D

Description

Code from chapter 15 of the book Learn Physics with Functional Programming

Synopsis

type Time = R
type TimeStep = R
type Mass = R
type Position = R
type Velocity = R
type Force = R
type State1D = (Time, Position, Velocity)
newtonSecond1D :: Mass -> [State1D -> Force] -> State1D -> (R, R, R)
euler1D :: R -> (State1D -> (R, R, R)) -> State1D -> State1D
updateTXV :: R -> Mass -> [State1D -> Force] -> State1D -> State1D
statesTXV :: R -> Mass -> State1D -> [State1D -> Force] -> [State1D]
velocity1D :: [State1D] -> Time -> Velocity
velocityFtxv :: R -> Mass -> State1D -> [State1D -> Force] -> Time -> Velocity
position1D :: [State1D] -> Time -> Position
positionFtxv :: R -> Mass -> State1D -> [State1D -> Force] -> Time -> Position
springForce :: R -> State1D -> Force
dampedHOForces :: [State1D -> Force]
dampedHOStates :: [State1D]
pingpongPosition :: Time -> Velocity
pingpongVelocity :: Time -> Velocity
eulerCromer1D :: R -> (State1D -> (R, R, R)) -> State1D -> State1D
updateTXVEC :: R -> Mass -> [State1D -> Force] -> State1D -> State1D
type UpdateFunction s = s -> s
type DifferentialEquation s ds = s -> ds
type NumericalMethod s ds = DifferentialEquation s ds -> UpdateFunction s
solver :: NumericalMethod s ds -> DifferentialEquation s ds -> s -> [s]
class RealVectorSpace ds where
- (+++) :: ds -> ds -> ds
- scale :: R -> ds -> ds
class RealVectorSpace ds => Diff s ds where
- shift :: R -> ds -> s -> s
euler :: Diff s ds => R -> (s -> ds) -> s -> s
rungeKutta4 :: Diff s ds => R -> (s -> ds) -> s -> s
exponential :: DifferentialEquation (R, R, R) (R, R, R)
update2 :: (R, R, R) -> (R, R, R)
earthGravity :: Mass -> State1D -> Force
type MState = (Time, Mass, Position, Velocity)
earthGravity2 :: MState -> Force
positionFtxv2 :: R -> MState -> [MState -> Force] -> Time -> Position
statesTXV2 :: R -> MState -> [MState -> Force] -> [MState]
updateTXV2 :: R -> [MState -> Force] -> MState -> MState
updateTV' :: R -> Mass -> [(Time, Velocity) -> Force] -> (Time, Velocity) -> (Time, Velocity)
forces :: R -> [State1D -> R]
vdp :: R -> [(R, R)]

Documentation

type Time = R Source #

type TimeStep = R Source #

type Mass = R Source #

type Position = R Source #

type Velocity = R Source #

type Force = R Source #

type State1D = (Time, Position, Velocity) Source #

newtonSecond1D :: Mass -> [State1D -> Force] -> State1D -> (R, R, R) Source #

euler1D :: R -> (State1D -> (R, R, R)) -> State1D -> State1D Source #

updateTXV :: R -> Mass -> [State1D -> Force] -> State1D -> State1D Source #

statesTXV :: R -> Mass -> State1D -> [State1D -> Force] -> [State1D] Source #

velocity1D :: [State1D] -> Time -> Velocity Source #

velocityFtxv :: R -> Mass -> State1D -> [State1D -> Force] -> Time -> Velocity Source #

position1D :: [State1D] -> Time -> Position Source #

positionFtxv :: R -> Mass -> State1D -> [State1D -> Force] -> Time -> Position Source #

springForce :: R -> State1D -> Force Source #

dampedHOForces :: [State1D -> Force] Source #

dampedHOStates :: [State1D] Source #

pingpongPosition :: Time -> Velocity Source #

pingpongVelocity :: Time -> Velocity Source #

eulerCromer1D :: R -> (State1D -> (R, R, R)) -> State1D -> State1D Source #

updateTXVEC :: R -> Mass -> [State1D -> Force] -> State1D -> State1D Source #

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.

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.

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 #

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.

exponential :: DifferentialEquation (R, R, R) (R, R, R) Source #

update2 :: (R, R, R) -> (R, R, R) Source #

earthGravity :: Mass -> State1D -> Force Source #

type MState = (Time, Mass, Position, Velocity) Source #

earthGravity2 :: MState -> Force Source #

positionFtxv2 :: R -> MState -> [MState -> Force] -> Time -> Position Source #

statesTXV2 :: R -> MState -> [MState -> Force] -> [MState] Source #

updateTXV2 :: R -> [MState -> Force] -> MState -> MState Source #

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

forces :: R -> [State1D -> R] Source #

vdp :: R -> [(R, R)] Source #