private static void EllasticColl()
{
var m1 = 4d;
var m2 = 6d;
var vx1 = 5d;
var vx2 = -5d;
var x1 = new Polynomial(0, 5);
var x2 = new Polynomial(10, -5);
var vy1 = 5d;
var vy2 = 0d;
var y1 = new Polynomial(0, 5);
var y2 = new Polynomial(5, 0);
var r1 = 0.5d;
var r2 = 0.5d;
var dx = (x2 - x1);
var dy = (y2 - y1);
var meetingPointsPol = (dx ^ 2) + (dy ^ 2) - System.Math.Pow(r1 + r2, 2);
var roots = FindRoots.Polynomial(meetingPointsPol.Coefficients);
var t = roots.Where(r => r.IsReal()).Select(r => r.Real).Min();
Vector2D v1 = new Vector2D(vx1, vy1);
Vector2D v2 = new Vector2D(vx2, vy2);
var tangent = new Vector2D(dx.Evaluate(t), dy.Evaluate(t)).Orthogonal.Normalize();
var v1t = v1.ProjectOn(tangent);
var u1t = v1t;
var v1p = v1 - v1t;
var v2t = v2.ProjectOn(tangent);
var u2t = v2t;
var v2p = v2 - v2t;
var p_p = m1 * v1p.Length + m2 * v2p.Length;
var e = 0.5 * m1 * System.Math.Pow(v1.Length, 2) + 0.5 * m2 * System.Math.Pow(v2.Length, 2);
var u1p = new Polynomial(p_p / m1, -m2 / m1);
var u2pLengths = (0.5 * m1 * ((u1p ^ 2) + System.Math.Pow(u1t.Length, 2)) +
0.5 * m2 * ((new Polynomial(0, 1) ^ 2) + System.Math.Pow(u2t.Length, 2))).Roots(e);
var u1pLength = u1p.Evaluate(u2pLengths.First());
}
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));
}
