public static double Solve(PolynomialFunction p, double guess, double tolerance, int maxIterations)
{
double x = guess;
double iter;
for (iter = 0; iter < maxIterations; iter++)
{
double delta = p.Evaluate(x) / p.Derivative(x);
if (Math.Abs(delta) < tolerance)
{
break;
}
x = x - delta;
}
if (iter == maxIterations)
{
throw new Exception("NewtonSolver reached iteration limit of " + maxIterations + " on polynomial " + p.ToString());
}
return(x);
}
public static void Solve(Vector3d R1, Vector3d R2, double dt, double gravParameter, bool shortway, out Vector3d V1, out Vector3d V2)
{
double muCB = gravParameter;
double R1mag = R1.magnitude;
double R2mag = R2.magnitude;
double tm;
if (shortway)
{
tm = 1.0;
}
else
{
tm = -1.0;
}
double cosDeltaTA = (Vector3d.Dot(R1, R2)) / (R1mag * R2mag);
double sinDeltaTA = tm * Math.Sqrt(1 - Math.Pow(cosDeltaTA, 2));
double deltaTA = Math.Atan2(sinDeltaTA, cosDeltaTA);
if (deltaTA < 0)
{
deltaTA = deltaTA + 2 * Math.PI;
}
double c = Math.Sqrt(Math.Pow(R1mag, 2) + Math.Pow(R2mag, 2) - 2 * R1mag * R2mag * cosDeltaTA);
double s = (R1mag + R2mag + c) / 2;
double epsilon = (R2mag - R1mag) / R1mag;
double intemed1 = R2mag / R1mag;
double TanSqr2w = (Math.Pow(epsilon, 2) / 4) / (Math.Sqrt(intemed1) + intemed1 * (2 + Math.Sqrt(intemed1)));
double sinSqrDeltaTAOver4 = Math.Pow(Math.Sin(deltaTA / 4), 2);
double cosSqrDeltaTAOver4 = Math.Pow(Math.Cos(deltaTA / 4), 2);
double rop = Math.Sqrt(R1mag * R2mag) * (cosSqrDeltaTAOver4 + TanSqr2w);
double l;
if (shortway)
{
l = (sinSqrDeltaTAOver4 + TanSqr2w) / (sinSqrDeltaTAOver4 + TanSqr2w + Math.Cos(deltaTA / 2));
}
else
{
l = (cosSqrDeltaTAOver4 + TanSqr2w - Math.Cos(deltaTA / 2)) / (cosSqrDeltaTAOver4 + TanSqr2w);
}
double m = (muCB * Math.Pow(dt, 2)) / (8 * Math.Pow(rop, 3));
double x = l;
double x_change = 1;
double y = 0;
int loops = 0;
do
{
double ksi = ComputeKsi(x, 8);
double h1 = (Math.Pow((l + x), 2) * (1 + 3 * x + ksi)) / ((1 + 2 * x + l) * (4 * x + ksi * (3 + x)));
double h2 = (m * (x - l + ksi)) / ((1 + 2 * x + l) * (4 * x + ksi * (3 + x)));
double[] polyConsts = { -h2, 0, -(1 + h1), 1 };
PolynomialFunction yEqnPoly = new PolynomialFunction(polyConsts);
//const double relativeAccuracy = 1.0e-12;
//const double absoluteAccuracy = 1.0e-12;
//BracketingNthOrderBrentSolver solver = new BracketingNthOrderBrentSolver(relativeAccuracy, absoluteAccuracy, 10);
//y = solver.solve(10000, yEqnPoly, -10000, 10000, 0.0, AllowedSolution.ANY_SIDE);
//replaced Arrowstar's above four commented lines with this solver: -The_Duck
//Use an initial guess of 10; NewtonSolver will get stuck with an initial guess of zero.
y = NewtonSolver.Solve(yEqnPoly, 10, 1.0e-12, 50);
double x_new = Math.Sqrt(Math.Pow((1 - l) / 2, 2) + m / Math.Pow(y, 2)) - (1 + l) / 2;
x_change = Math.Abs(x - x_new);
x = x_new;
loops++;
} while (x_change > Math.Pow(10, -6) && loops < 30);
double a = (muCB * Math.Pow(dt, 2)) / (16 * Math.Pow(rop, 2) * x * Math.Pow(y, 2));
double f = 0;
double g = 0;
double g_dot = 0;
const double small = 1e-5;
if (a > small)
{
double sinBetaEOver2 = Math.Sqrt((s - c) / (2 * a));
double betaE = 2 * Math.Asin(sinBetaEOver2);
if (deltaTA > Math.PI)
{
betaE = -betaE;
}
double amin = s / 2;
double tmin = Math.Sqrt(Math.Pow(amin, 3) / muCB) * (Math.PI - betaE + Math.Sin(betaE));
double alphaE = 2 * Math.Asin(Math.Sqrt(s / (2 * a)));
if (dt > tmin)
{
alphaE = 2 * Math.PI - alphaE;
}
double deltaE = alphaE - betaE;
f = 1 - (a / R1mag) * (1 - Math.Cos(deltaE));
g = dt - Math.Sqrt(Math.Pow(a, 3) / muCB) * (deltaE - Math.Sin(deltaE));
g_dot = 1 - (a / R2mag) * (1 - Math.Cos(deltaE));
}
else if (a < -small)
{
//Asinh asinh=new Asinh();
//double alphaH = 2*asinh.value(Math.Sqrt(s/(-2*a)));
//double betaH = 2*asinh.value(Math.Sqrt((s-c)/(-2*a)));
//Porting Arrowstar's above three lines to: -The_Duck
double alphaH = 2 * MuUtils.Asinh(Math.Sqrt(s / (-2 * a)));
double betaH = 2 * MuUtils.Asinh(Math.Sqrt((s - c) / (-2 * a)));
double deltaH = alphaH - betaH;
f = 1 - (a / R1mag) * (1 - Math.Cosh(deltaH));
g = dt - Math.Sqrt(-Math.Pow(a, 3) / muCB) * (Math.Sinh(deltaH) - deltaH);
g_dot = 1 - (a / R2mag) * (1 - Math.Cosh(deltaH));
}
else
{
//List<Vector3d> VArr = null;
//commented out the above line from Arrowstar's original, since it seems to do nothing and throws a compiler error -The_Duck
}
V1 = (R2 - (f * R1)) / g;
V2 = (g_dot * R2 - R1) / g;
}
public static void Solve(Vector3d R1, Vector3d R2, double dt, CelestialBody primary, bool shortway, out Vector3d V1, out Vector3d V2)
{
double muCB = primary.gravParameter;
double R1mag = R1.magnitude;
double R2mag = R2.magnitude;
double tm;
if (shortway)
{
tm = 1.0;
}
else
{
tm = -1.0;
}
double cosDeltaTA = (Vector3d.Dot(R1, R2)) / (R1mag * R2mag);
double sinDeltaTA = tm * Math.Sqrt(1 - Math.Pow(cosDeltaTA, 2));
double deltaTA = Math.Atan2(sinDeltaTA, cosDeltaTA);
if (deltaTA < 0)
{
deltaTA = deltaTA + 2 * Math.PI;
}
double c = Math.Sqrt(Math.Pow(R1mag, 2) + Math.Pow(R2mag, 2) - 2 * R1mag * R2mag * cosDeltaTA);
double s = (R1mag + R2mag + c) / 2;
double epsilon = (R2mag - R1mag) / R1mag;
double intemed1 = R2mag / R1mag;
double TanSqr2w = (Math.Pow(epsilon, 2) / 4) / (Math.Sqrt(intemed1) + intemed1 * (2 + Math.Sqrt(intemed1)));
double sinSqrDeltaTAOver4 = Math.Pow(Math.Sin(deltaTA / 4), 2);
double cosSqrDeltaTAOver4 = Math.Pow(Math.Cos(deltaTA / 4), 2);
double rop = Math.Sqrt(R1mag * R2mag) * (cosSqrDeltaTAOver4 + TanSqr2w);
double l;
if (shortway)
{
l = (sinSqrDeltaTAOver4 + TanSqr2w) / (sinSqrDeltaTAOver4 + TanSqr2w + Math.Cos(deltaTA / 2));
}
else
{
l = (cosSqrDeltaTAOver4 + TanSqr2w - Math.Cos(deltaTA / 2)) / (cosSqrDeltaTAOver4 + TanSqr2w);
}
double m = (muCB * Math.Pow(dt, 2)) / (8 * Math.Pow(rop, 3));
double x = l;
double x_change = 1;
double y = 0;
int loops = 0;
do
{
double ksi = ComputeKsi(x, 8);
double h1 = (Math.Pow((l + x), 2) * (1 + 3 * x + ksi)) / ((1 + 2 * x + l) * (4 * x + ksi * (3 + x)));
double h2 = (m * (x - l + ksi)) / ((1 + 2 * x + l) * (4 * x + ksi * (3 + x)));
double[] polyConsts = { -h2, 0, -(1 + h1), 1 };
PolynomialFunction yEqnPoly = new PolynomialFunction(polyConsts);
//const double relativeAccuracy = 1.0e-12;
//const double absoluteAccuracy = 1.0e-12;
//BracketingNthOrderBrentSolver solver = new BracketingNthOrderBrentSolver(relativeAccuracy, absoluteAccuracy, 10);
//y = solver.solve(10000, yEqnPoly, -10000, 10000, 0.0, AllowedSolution.ANY_SIDE);
//replaced Arrowstar's above four commented lines with this solver: -The_Duck
//Use an initial guess of 10; NewtonSolver will get stuck with an initial guess of zero.
y = NewtonSolver.Solve(yEqnPoly, 10, 1.0e-12, 50);
double x_new = Math.Sqrt(Math.Pow((1 - l) / 2, 2) + m / Math.Pow(y, 2)) - (1 + l) / 2;
x_change = Math.Abs(x - x_new);
x = x_new;
loops++;
} while (x_change > Math.Pow(10, -6) && loops < 30);
double a = (muCB * Math.Pow(dt, 2)) / (16 * Math.Pow(rop, 2) * x * Math.Pow(y, 2));
double f = 0;
double g = 0;
double g_dot = 0;
double small = 1e-5;
if (a > small)
{
double sinBetaEOver2 = Math.Sqrt((s - c) / (2 * a));
double betaE = 2 * Math.Asin(sinBetaEOver2);
if (deltaTA > Math.PI)
{
betaE = -betaE;
}
double amin = s / 2;
double tmin = Math.Sqrt(Math.Pow(amin, 3) / muCB) * (Math.PI - betaE + Math.Sin(betaE));
double alphaE = 2 * Math.Asin(Math.Sqrt(s / (2 * a)));
if (dt > tmin)
{
alphaE = 2 * Math.PI - alphaE;
}
double deltaE = alphaE - betaE;
f = 1 - (a / R1mag) * (1 - Math.Cos(deltaE));
g = dt - Math.Sqrt(Math.Pow(a, 3) / muCB) * (deltaE - Math.Sin(deltaE));
g_dot = 1 - (a / R2mag) * (1 - Math.Cos(deltaE));
}
else if (a < -small)
{
//Asinh asinh=new Asinh();
//double alphaH = 2*asinh.value(Math.Sqrt(s/(-2*a)));
//double betaH = 2*asinh.value(Math.Sqrt((s-c)/(-2*a)));
//Porting Arrowstar's above three lines to: -The_Duck
double alphaH = 2 * MuUtils.Asinh(Math.Sqrt(s / (-2 * a)));
double betaH = 2 * MuUtils.Asinh(Math.Sqrt((s - c) / (-2 * a)));
double deltaH = alphaH - betaH;
f = 1 - (a / R1mag) * (1 - Math.Cosh(deltaH));
g = dt - Math.Sqrt(-Math.Pow(a, 3) / muCB) * (Math.Sinh(deltaH) - deltaH);
g_dot = 1 - (a / R2mag) * (1 - Math.Cosh(deltaH));
}
else
{
//List<Vector3d> VArr = null;
//commented out the above line from Arrowstar's original, since it seems to do nothing and throws a compiler error -The_Duck
}
V1 = (R2 - f * R1) / g;
V2 = (g_dot * R2 - R1) / g;
}
public static double Solve(PolynomialFunction p, double guess, double tolerance, int maxIterations)
{
double x = guess;
double iter;
for (iter = 0; iter < maxIterations; iter++)
{
double delta = p.Evaluate(x) / p.Derivative(x);
if (Math.Abs(delta) < tolerance) break;
x = x - delta;
}
if (iter == maxIterations)
{
throw new Exception("NewtonSolver reached iteration limit of " + maxIterations + " on polynomial " + p.ToString());
}
return x;
}
