public override ISimulation <RocketSimulationMoment> GenerateSimulation(double t1, double t2)
{
double burnTime = t1 + _propellantMass / _massLossRate;
var xa = new IntervalIndexer <Func <double, double> >();
xa.AddInterval((Endpoints.Closed(t1), Endpoints.Closed(burnTime)),
(t) => RocketAEquation(t, t1));
xa.AddInterval((Endpoints.Open(burnTime), Endpoints.Unbounded),
(t) => 0);
var xv = new IntervalIndexer <Func <double, double> >();
xv.AddInterval((Endpoints.Closed(t1), Endpoints.Closed(burnTime)),
(t) => RocketVEquation(t, t1));
xv.AddInterval((Endpoints.Open(burnTime), Endpoints.Unbounded),
(t) => RocketVEquation(burnTime, t1));
var x = new IntervalIndexer <Func <double, double> >();
x.AddInterval((Endpoints.Closed(t1), Endpoints.Closed(burnTime)),
(t) => RocketXEquation(t, t1));
x.AddInterval((Endpoints.Open(burnTime), Endpoints.Unbounded),
(t) => RocketXEquation(burnTime, t1) + RocketVEquation(burnTime, t1) * (t - burnTime));
return(new RocketSimulation(_baseMass, _propellantMass, _massLossRate, burnTime, xa, xv, x));
}
public override ISimulation <AngularMomentumSimulationMoment> GenerateSimulation(double t1, double t2)
{
var(massByR, radius) = (_disc.SpecificMassByR, _disc.Radius);
var momentOfInertiaByR = massByR * new Polynomial(0, 0, 1);
var momentOfInertia = momentOfInertiaByR.DefiniteIntegral(radius);
var angularAcceleration = (_force * radius) / momentOfInertia;
var angleOverTime = (new Polynomial(angularAcceleration)).AntiDerivative(_angularVel0).AntiDerivative();
var anglet = new IntervalIndexer <Polynomial>();
anglet.AddInterval((Endpoints.Closed(t1), Endpoints.Closed(t2)), angleOverTime);
var defaultIndexer = new IntervalIndexer <Polynomial>(new Polynomial());
return(new AngularMomentumSimulation(_disc, defaultIndexer, anglet, defaultIndexer, defaultIndexer));
}
public override ISimulation <AngularMomentumSimulationMoment> GenerateSimulation(double t1, double t2)
{
var vt = new IntervalIndexer <Polynomial>();
var xt = new IntervalIndexer <Polynomial>();
var omegat = new IntervalIndexer <Polynomial>();
var anglet = new IntervalIndexer <Polynomial>();
var v = new Polynomial(_v0);
var omega = new Polynomial(_omega0);
var vOnSurface = v + omega * _disk.Radius;
var t = t1;
var vOnSurface0 = vOnSurface.Evaluate(t);
// There's friction that acts on the disk
if (vOnSurface0.CompareTo(0, 6e-5) != 0)
{
var circumferenceByR = new Polynomial(0, 2 * System.Math.PI);
var tMass = (circumferenceByR * _disk.SpecificMassByR).DefiniteIntegral(_disk.Radius);
var rSquared = new Polynomial(0, 0, 1);
var iZ = ((circumferenceByR * _disk.SpecificMassByR) * rSquared).DefiniteIntegral(_disk.Radius);
var friction = (-System.Math.Sign(vOnSurface0)) * (_coOfKineticFriction * tMass * g0);
var torque = _disk.Radius * friction;
var angularAcceleration = torque / iZ;
omega = (new Polynomial(angularAcceleration)).AntiDerivative(_omega0);
var a = friction / tMass;
v = (new Polynomial(a)).AntiDerivative(_v0);
vOnSurface = v + omega * _disk.Radius;
var tf = t2;
try
{
tf = vOnSurface.Roots(0, t1, t2).First();
}
catch (InvalidOperationException)
{
}
var slipInterval = (Endpoints.Closed(t), Endpoints.Open(tf));
vt.AddInterval(slipInterval, v);
xt.AddInterval(slipInterval, v.AntiDerivative());
omegat.AddInterval(slipInterval, omega);
anglet.AddInterval(slipInterval, omega.AntiDerivative());
t = tf;
}
if (t < t2)
{
var noSlipInterval = (Endpoints.Closed(t), Endpoints.Unbounded);
vt.AddInterval(
noSlipInterval,
new Polynomial(v.Evaluate(t))
);
xt.AddInterval(
noSlipInterval,
new Polynomial(v.AntiDerivative().Evaluate(t), v.Evaluate(t))
.Offset(-t)
);
omegat.AddInterval(
noSlipInterval,
new Polynomial(omega.Evaluate(t))
);
anglet.AddInterval(
noSlipInterval,
new Polynomial(omega.AntiDerivative().Evaluate(t), omega.Evaluate(t))
.Offset(-t)
);
}
return(new AngularMomentumSimulation(_disk, omegat, anglet, vt, xt));
}