57 lines
1.8 KiB
Haskell
57 lines
1.8 KiB
Haskell
-- SPDX-License-Identifier: ISC
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-- Copyright (c) 2020 Camden Dixie O'Brien
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module Main (main) where
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import Graphics.Gloss
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import Graphics.Gloss.Geometry.Angle
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data PolarCoord = PolarCoord { radius :: Float, angle :: Float }
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data State = State { position :: PolarCoord
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, radialMomentum :: Float
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, angularMomentum :: Float }
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majorMass :: Float
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majorMass = 200
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minorMass :: Float
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minorMass = 20
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initialState :: State
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initialState = State (PolarCoord 300 0) 0 0.001
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framesPerSecond :: Int
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framesPerSecond = 120
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render :: State -> Picture
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render state = pictures [ circleSolid (sqrt majorMass)
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, translatePolar (position state) $ circleSolid (sqrt minorMass) ]
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step :: a -> b -> State -> State
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step _ _ state = state { position = nextPosition state
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, radialMomentum = nextRadialMomentum state }
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nextPosition :: State -> PolarCoord
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nextPosition state = let r = radius . position $ state
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a = angle . position $ state
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rDot = radialMomentum state / minorMass
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aDot = angularMomentum state / (minorMass * r ^ 2)
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in PolarCoord (r + rDot) (a + aDot)
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nextRadialMomentum :: State -> Float
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nextRadialMomentum state = let r = radius . position $ state
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p = radialMomentum state
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l = angularMomentum state
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pDot = (l ^ 2 / (2 * minorMass * r) - minorMass * majorMass) / r ^ 2
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in p + pDot
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translatePolar :: PolarCoord -> Picture -> Picture
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translatePolar q = rotate (radToDeg $ angle q) . translate (radius q) 0
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window :: Display
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window = InWindow "Foo" (800, 800) (100, 100)
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main :: IO ()
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main = simulate window white framesPerSecond initialState render step
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