/// <summary>
/// Compute the transfer time for the minimum energy transfer.
/// </summary>
/// <returns></returns>
private double ComputeMinTime(ref double[] r0, ref double[] r, NBody centerBody, bool shortPath)
{
// Fundamentals of Astrodynamics and Applications, Vallado, 4th Ed., Algorithm 56 p475
// Take r0, r => a_min, e_min, t_min
// This approach assumes r > r0.
// If we have r0 > r then need to flip them and then reverse the velocities when doing the
// maneuver determination
double[] center = new double[] { 0, 0, 0 };
GravityEngine ge = GravityEngine.Instance();
ge.GetPositionDouble(centerBody, ref center);
Vector3d center3d = new Vector3d(ref center);
Vector3d r0_vec = new Vector3d(ref r0) - center3d;
Vector3d r_vec = new Vector3d(ref r) - center3d;
double r0_mag = Vector3d.Magnitude(r0_vec);
double r_mag = Vector3d.Magnitude(r_vec);
double cos_delta_nu = Vector3d.Dot(r0_vec, r_vec) / (r0_mag * r_mag);
double c = System.Math.Sqrt(r0_mag * r0_mag + r_mag * r_mag
- 2 * r0_mag * r_mag * cos_delta_nu);
double s = (r0_mag + r_mag + c) / 2;
a_min = s / 2;
// double p_min = r0_mag * r_mag * (1 - cos_delta_nu) / c;
// e_min = System.Math.Sqrt(1 - 2 * p_min / s);
// alpha for elliptical xfer, min energy
double alpha_e = System.Math.PI;
// p471: set beta_e negative if delta_nu > 18
double beta_e = 2.0 * System.Math.Asin(System.Math.Sqrt((s - c) / s));
// t_min for a_min
// +/- in front of (beta_e...). Which sign? Negative for shorter path.
double sign = -1;
if (!shortPath)
{
sign = 1;
}
t_min = System.Math.Sqrt(a_min * a_min * a_min / mu) * (alpha_e + sign * (beta_e - System.Math.Sin(beta_e)));
return(t_min);
}
/// <summary>
/// Setup for Lambert Universal construction. Calculation is done via ComputeXfer and may be
/// done more than once for different transit times.
///
/// Initial conditions are passed in when created.
///
/// The transfer assumes there is an active NBody at the fromOrbit to be maneuvered to the
/// orbit specified by the toOrbit. One of the from/to orbit data elements must have a
/// centerNBody.
///
/// </summary>
/// <param name="fromOrbit"></param>
/// <param name="toOrbit"></param>
/// <param name="shortPath">Take shortest path along the ellipse (if xfer is an ellipse)</param>
public LambertUniversal(OrbitData _fromOrbit, OrbitData _toOrbit, bool shortPath) : base(_fromOrbit, _toOrbit)
{
name = "LambertUniversal";
// Fundamentals of Astrodynamics and Applications, Vallado, 4th Ed., Algorithm 56 p475
// Take r0, r => a_min, e_min, t_min, v0
double[] r1_array = new double[] { 0, 0, 0 };
double[] r2_array = new double[] { 0, 0, 0 };
double[] center = new double[] { 0, 0, 0 };
GravityEngine ge = GravityEngine.Instance();
// If Nbody is available get position directly. If not (target marker) then
// use orbit phase to compute position
ge.GetPositionDouble(centerBody, ref center);
center3d = new Vector3d(ref center);
if (fromOrbit.nbody != null)
{
ge.GetPositionDouble(fromOrbit.nbody, ref r1_array);
}
else
{
Vector3 pos = toOrbit.GetPhysicsPositionforEllipse(fromOrbit.phase);
r1_array = new double[] { pos.x, pos.y, pos.z };
}
if (toOrbit.nbody != null)
{
ge.GetPositionDouble(toOrbit.nbody, ref r2_array);
}
else
{
Vector3 pos = toOrbit.GetPhysicsPositionforEllipse(toOrbit.phase);
r2_array = new double[] { pos.x, pos.y, pos.z };
}
r1 = new Vector3d(ref r1_array) - center3d;
r2 = new Vector3d(ref r2_array) - center3d;
if (fromOrbit.a < toOrbit.a)
{
innerOrbit = fromOrbit;
outerOrbit = toOrbit;
innerToOuter = true;
}
else
{
innerOrbit = toOrbit;
outerOrbit = fromOrbit;
innerToOuter = false;
}
mu = ge.GetPhysicsMass(fromOrbit.centralMass);
// determine t_min.
// If Nbody is available get position directly. If not (target marker) then
// use orbit phase to compute position
double[] r0 = new double[] { 0, 0, 0 };
double[] r = new double[] { 0, 0, 0 };
if (innerOrbit.nbody != null)
{
ge.GetPositionDouble(innerOrbit.nbody, ref r0);
}
else
{
Vector3 pos = toOrbit.GetPhysicsPositionforEllipse(innerOrbit.phase);
r0 = new double[] { pos.x, pos.y, pos.z };
}
if (outerOrbit.nbody != null)
{
ge.GetPositionDouble(outerOrbit.nbody, ref r);
}
else
{
Vector3 pos = toOrbit.GetPhysicsPositionforEllipse(outerOrbit.phase);
r = new double[] { pos.x, pos.y, pos.z };
}
ComputeMinTime(ref r0, ref r, fromOrbit.centralMass, shortPath);
}