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Implement hamiltonian simulation

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Camden Dixie O'Brien 2021-01-01 00:00:39 +00:00
parent daeff1c461
commit 874edf17f2
1 changed files with 19 additions and 1 deletions
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20
Main.hs
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@ -32,5 +32,23 @@ rod = color rodColor $ line [ (0, 0), (0, negate rodLength) ]
particle = color particleColor $ circleSolid particleRadius particle = color particleColor $ circleSolid particleRadius
rotateRadians = rotate . radToDeg . negate rotateRadians = rotate . radToDeg . negate
step _ _ = nextState
nextState state = State (theta state + thetaDot state)
(pTheta state + pThetaDot state)
(phi state + phiDot state)
(pPhi state + pPhiDot state)
thetaDot state
= (6 * (2 * pTheta state - 3 * cos (theta state - phi state) * pPhi state))
/ (particleMass * rodLength ^ 2 * (16 - 9 * cos (theta state - phi state) ^ 2))
phiDot state
= (6 * (8 * pPhi state - 3 * cos (theta state - phi state) * pTheta state))
/ (particleMass * rodLength ^ 2 * (16 - 9 * cos (theta state - phi state) ^ 2))
pThetaDot state
= (- 1 / 2) * particleMass * rodLength ^ 2
* (thetaDot state * phiDot state * sin (theta state - phi state) + 3 * g * sin (theta state) / rodLength)
pPhiDot state
= (1 / 2) * particleMass * rodLength ^ 2
* (thetaDot state * phiDot state * sin (theta state - phi state) - g * sin (phi state) / rodLength)
window = InWindow "Double Pendulum" (800, 800) (100, 100) window = InWindow "Double Pendulum" (800, 800) (100, 100)
main = display window white (render initialState) main = simulate window white framesPerSecond initialState render step