module Drasil.Projectile.Derivations (
  timeDeriv,
  landPosDeriv,
  rectVelDeriv,
  rectPosDeriv,
  horMotionDeriv, horMotionEqn1, horMotionEqn2,
  verMotionDeriv, verMotionEqn1, verMotionEqn2, verMotionEqn3
) where

import Prelude hiding (cos, sin)

import Language.Drasil (eqSymb, LiteralC(..), ModelExprC(..), ExprC(..),
  ModelExpr, square, half)
import qualified Data.Drasil.Quantities.Physics as QP (iSpeed,
  constAccel, ixPos, iyPos)
import Data.Drasil.Quantities.Physics (gravitationalAccel, gravitationalAccelConst,
  iPos, ixVel, iyVel, scalarPos, speed, time, xPos, xVel, yPos, yVel, ixSpeed, iySpeed)

import Drasil.Projectile.Unitals (launAngle, launSpeed, landPos, flightDur)

--
timeDeriv :: [ModelExpr]
timeDeriv :: [ModelExpr]
timeDeriv = [ModelExpr
timeDerivEqn1, ModelExpr
timeDerivEqn2, ModelExpr
timeDerivEqn3, ModelExpr
timeDerivEqn4]

timeDerivEqn1, timeDerivEqn2, timeDerivEqn3, timeDerivEqn4 :: ModelExpr
timeDerivEqn1 :: ModelExpr
timeDerivEqn1 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
yPos ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iyVel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$- ModelExpr -> ModelExpr
forall r. (ExprC r, LiteralC r) => r -> r
half (ConstQDef -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstQDef
gravitationalAccelConst ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ModelExpr -> ModelExpr
forall r. (ExprC r, LiteralC r) => r -> r
square (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time))
timeDerivEqn2 :: ModelExpr
timeDerivEqn2 = (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iyVel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
flightDur) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$- ModelExpr -> ModelExpr
forall r. (ExprC r, LiteralC r) => r -> r
half (ConstQDef -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstQDef
gravitationalAccelConst ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ModelExpr -> ModelExpr
forall r. (ExprC r, LiteralC r) => r -> r
square (ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
flightDur)) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 0
timeDerivEqn3 :: ModelExpr
timeDerivEqn3 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iyVel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$- ModelExpr -> ModelExpr
forall r. (ExprC r, LiteralC r) => r -> r
half (ConstQDef -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstQDef
gravitationalAccelConst ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
flightDur) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 0
timeDerivEqn4 :: ModelExpr
timeDerivEqn4 = ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
flightDur ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 2 ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iyVel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$/ ConstQDef -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstQDef
gravitationalAccelConst

--
landPosDeriv :: [ModelExpr]
landPosDeriv :: [ModelExpr]
landPosDeriv = [ModelExpr
landPosDerivEqn1, ModelExpr
landPosDerivEqn2, ModelExpr
landPosDerivEqn3]

landPosDerivEqn1, landPosDerivEqn2, landPosDerivEqn3 :: ModelExpr
landPosDerivEqn1 :: ModelExpr
landPosDerivEqn1 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
xPos    ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
ixVel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time
landPosDerivEqn2 :: ModelExpr
landPosDerivEqn2 = ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
landPos ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
ixVel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 2 ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
launSpeed ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ModelExpr -> ModelExpr
forall r. ExprC r => r -> r
sin (ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
launAngle) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$/ ConstQDef -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstQDef
gravitationalAccelConst
landPosDerivEqn3 :: ModelExpr
landPosDerivEqn3 = ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
landPos ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
launSpeed ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ModelExpr -> ModelExpr
forall r. ExprC r => r -> r
cos (ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
launAngle) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 2 ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
launSpeed ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ModelExpr -> ModelExpr
forall r. ExprC r => r -> r
sin (ConstrConcept -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstrConcept
launAngle) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$/ ConstQDef -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy ConstQDef
gravitationalAccelConst


--
rectVelDeriv :: [ModelExpr]
rectVelDeriv :: [ModelExpr]
rectVelDeriv = [ModelExpr
rectVelDerivEqn1, ModelExpr
rectVelDerivEqn2]

rectVelDerivEqn1, rectVelDerivEqn2 :: ModelExpr
rectVelDerivEqn1 :: ModelExpr
rectVelDerivEqn1 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
QP.constAccel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= ModelExpr -> UnitalChunk -> ModelExpr
forall r c. (ModelExprC r, HasUID c, HasSymbol c) => r -> c -> r
deriv (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
speed) UnitalChunk
time
rectVelDerivEqn2 :: ModelExpr
rectVelDerivEqn2 = Symbol -> ModelExpr -> ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => Symbol -> r -> r -> r -> r
defint (UnitalChunk -> Symbol
forall q. HasSymbol q => q -> Symbol
eqSymb UnitalChunk
speed) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
QP.iSpeed) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
speed) (Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 1) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$=
                   Symbol -> ModelExpr -> ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => Symbol -> r -> r -> r -> r
defint (UnitalChunk -> Symbol
forall q. HasSymbol q => q -> Symbol
eqSymb UnitalChunk
time) (Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 0) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
QP.constAccel)

--
rectPosDeriv :: [ModelExpr]
rectPosDeriv :: [ModelExpr]
rectPosDeriv = [ModelExpr
rectPosDerivEqn1, ModelExpr
rectPosDerivEqn2, ModelExpr
rectPosDerivEqn3]

rectPosDerivEqn1, rectPosDerivEqn2, rectPosDerivEqn3 :: ModelExpr
rectPosDerivEqn1 :: ModelExpr
rectPosDerivEqn1 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
speed ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= ModelExpr -> UnitalChunk -> ModelExpr
forall r c. (ModelExprC r, HasUID c, HasSymbol c) => r -> c -> r
deriv (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
scalarPos) UnitalChunk
time
rectPosDerivEqn2 :: ModelExpr
rectPosDerivEqn2 = Symbol -> ModelExpr -> ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => Symbol -> r -> r -> r -> r
defint (UnitalChunk -> Symbol
forall q. HasSymbol q => q -> Symbol
eqSymb UnitalChunk
scalarPos) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iPos) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
scalarPos) (Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 1) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$=
                   Symbol -> ModelExpr -> ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => Symbol -> r -> r -> r -> r
defint (UnitalChunk -> Symbol
forall q. HasSymbol q => q -> Symbol
eqSymb UnitalChunk
time) (Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 0) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
speed)
rectPosDerivEqn3 :: ModelExpr
rectPosDerivEqn3 = Symbol -> ModelExpr -> ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => Symbol -> r -> r -> r -> r
defint (UnitalChunk -> Symbol
forall q. HasSymbol q => q -> Symbol
eqSymb UnitalChunk
scalarPos) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iPos) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
scalarPos) (Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 1) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$=
                   Symbol -> ModelExpr -> ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => Symbol -> r -> r -> r -> r
defint (UnitalChunk -> Symbol
forall q. HasSymbol q => q -> Symbol
eqSymb UnitalChunk
time) (Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 0) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time) (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
QP.iSpeed ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`addRe` (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
QP.constAccel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time))

--
horMotionDeriv :: [ModelExpr]
horMotionDeriv :: [ModelExpr]
horMotionDeriv = [ModelExpr
horMotionEqn1, ModelExpr
horMotionEqn2]

horMotionEqn1, horMotionEqn2 :: ModelExpr
horMotionEqn1 :: ModelExpr
horMotionEqn1 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
xVel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
ixSpeed
horMotionEqn2 :: ModelExpr
horMotionEqn2 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
xPos ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
QP.ixPos ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`addRe` (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
ixSpeed ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time)

--
verMotionDeriv :: [ModelExpr]
verMotionDeriv :: [ModelExpr]
verMotionDeriv = [ModelExpr
verMotionEqn1, ModelExpr
verMotionEqn2, ModelExpr
verMotionEqn3]

verMotionEqn1, verMotionEqn2, verMotionEqn3 :: ModelExpr
verMotionEqn1 :: ModelExpr
verMotionEqn1 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
yVel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iySpeed ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$- (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
gravitationalAccel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time)
verMotionEqn2 :: ModelExpr
verMotionEqn2 = UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
yPos ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
QP.iyPos ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`addRe` (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iySpeed ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$- (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
gravitationalAccel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` ModelExpr -> ModelExpr
forall r. (ExprC r, LiteralC r) => r -> r
square (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
time) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$/ Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 2)
verMotionEqn3 :: ModelExpr
verMotionEqn3 = ModelExpr -> ModelExpr
forall r. (ExprC r, LiteralC r) => r -> r
square (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
yVel) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$= ModelExpr -> ModelExpr
forall r. (ExprC r, LiteralC r) => r -> r
square (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
iySpeed) ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$- (Integer -> ModelExpr
forall r. LiteralC r => Integer -> r
exactDbl 2 ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
gravitationalAccel ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
`mulRe` (UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
yPos ModelExpr -> ModelExpr -> ModelExpr
forall r. ExprC r => r -> r -> r
$- UnitalChunk -> ModelExpr
forall r c. (ExprC r, HasUID c, HasSymbol c) => c -> r
sy UnitalChunk
QP.iyPos))