<div dir="ltr">Hello,<div style>I'm trying to write some simulator of </div><div style>physical systems using Yampa.</div><div style>The fundamental idea is to integrate </div><div style>the position and velocity, using</div>
<div style>the following algorithm:</div><div style><br></div><div style>1. get the velocity using the formula,</div><div style><br></div><div style>v = v0 + integral ( 0.5 * force * recip mass)</div><div style><br></div>
<div style>where v0 is the previous velocity.</div><div style><br></div><div style>2. calculate the new position as follows,</div><div style><br></div><div style>x = x0 + integral (v)</div><div style><br></div><div style>
and some other steps that are not relevant here.</div><div style>Therefore I wrote the following piece of </div><div style>code:</div><div style><br></div><div style><div>type Pos = Double</div><div>type Vel = Double</div>
<div>type Mass = Double</div><div>type Force = Double</div></div><div style><br></div><div style><div>integralCoordSF :: Force -> Mass -> SF (Pos,Vel) (Pos,Vel)</div><div>integralCoordSF force mass = proc (x0,v0) -> do</div>
<div> v <- integralVelSF force mass -< v0</div><div> vdt2 <- integral -< v</div><div> let x = x0 + vdt2</div><div>
returnA -< (x,v)</div><div> </div><div>integralVelSF :: Force -> Mass -> SF Double Double </div><div>integralVelSF force mass = proc v0 -> do</div><div> t1 <- integral -< 0.5 * (force/mass)</div>
<div> returnA -< v0 + t1</div><div><br></div><div><br></div><div style>Now, let's the speed (velocity), force and the mass equal 1.0. And</div><div style>the initial potion equal zero. Then using the "embed" function we get that,</div>
<div><br></div><div><div>*Main> embed (integralCoordSF 1.0 1.0) ((0.0,1.0),[(0.1,Nothing),(0.1,Nothing)])</div><div>[(0.0,1.0),(0.1,1.05),(0.20500000000000002,1.1)]</div></div><div><br></div><div style>According to the algorithm, if dt = 0.1 then </div>
<div style><br></div><div style>v = 1.0 + integral (0.5 * 1.0 * recip 1.0) = 1.05</div><div style><br></div><div style>in agreement with the algorithm. But let's see about the position</div><div style><br></div><div style>
x = 0 + integral (v) </div><div style><br></div><div style>Using the formula of step 2, the position should be equal to 0.105,</div><div style>but the result given by embed is 0.1.</div><div style><br></div><div style>As a beginner certainly and missing a lot of concepts and details,</div>
<div style>can someone please explain me what's going on here?</div><div style><br></div><div style>Thank you for your help!</div><div style><br></div><div style>Felipe Z</div><div style><br></div><div style> </div><div>
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