/// <summary>
/// Ephemeris computation
/// </summary>
/// <param name="Y0"></param>
/// <param name="N_Step"></param>
/// <param name="Step"></param>
/// <param name="p"></param>
/// <param name="Eph"></param>
static void Ephemeris(Geo.Algorithm.Vector Y0, int N_Step, double Step, ForceModelOption p, Geo.Algorithm.Vector[] Eph)
{
int i;
double t, t_end;
double relerr, abserr; // Accuracy requirements
DeIntegrator Orb = new DeIntegrator(Deriv, 6, p); // Object for integrating the eq. of motion
Geo.Algorithm.Vector Y = new Geo.Algorithm.Vector(Y0);
relerr = 1.0e-13;
abserr = 1.0e-6;
t = 0.0;
// Y = Y0;
Orb.Init(t, relerr, abserr);
for (i = 0; i <= N_Step; i++)
{
t_end = Step * i;
var Yresult = Orb.Integ(t_end, Y);
Eph[i] = Yresult;
}
;
//var prevObj = Eph[0];
//Console.WriteLine(prevObj);
//var last = Eph[Eph.Length -1];
//Console.WriteLine(last);
}
static void Main0(string[] args)
{
// Constants
const double GM = 1.0; // Gravitational coefficient
const double e = 0.9; // Eccentricity
const double t_end = 20.0; // End time
Geo.Algorithm.Vector Kep = new Geo.Algorithm.Vector(1.0, e, 0.0, 0.0, 0.0, 0.0); // (a,e,i,Omega,omega,M)
Geo.Algorithm.Vector y_ref = Kepler.State(GM, Kep, t_end); // Reference solution
// Variables
double t; // Time
double relerr, abserr; // Accuracy requirements
Geo.Algorithm.Vector y = new Geo.Algorithm.Vector(6); // State vector
AuxDataRecord Aux = new AuxDataRecord(); // Auxiliary satData
DeIntegrator Orbit = new DeIntegrator(f_Kep6D_, 6, Aux); // Object for integrating the
// differential equation
// defined by f_Kep6D_
// Header
var info = "Exercise 4-3: Step size control of DE multistep method" + "\r\n";
info += " Step t h r " + "\r\n";
Console.WriteLine(info);
// Initial values
t = 0.0;
y = new Geo.Algorithm.Vector(1.0 - e, 0.0, 0.0, 0.0, Math.Sqrt((1 + e) / (1 - e)), 0.0);
Aux.n_step = 0;
Aux.t = 0;
relerr = 0.0;
abserr = 1.0e-8;
// Integration from t=t to t=t_end
Orbit.Init(t, relerr, abserr);
Orbit.Integ(t_end, y);
Console.ReadKey();
}
static void Main(string[] args)
{
// Constants
const double relerr = 1.0e-13; // Relative and absolute
const double abserr = 1.0e-6; // accuracy requirement
const double a = OrbitConsts.RadiusOfEarth + 650.0e3; // Semi-major axis [m]
const double e = 0.001; // Eccentricity
const double inc = OrbitConsts.RadPerDeg * 51.0; // Inclination [rad]
double n = Math.Sqrt(OrbitConsts.GM_Earth / (a * a * a)); // Mean motion
Matrix Scale = Matrix.CreateDiagonal(new Geo.Algorithm.Vector(1, 1, 1, 1 / n, 1 / n, 1 / n)); // Velocity
Matrix scale = Matrix.CreateDiagonal(new Geo.Algorithm.Vector(1, 1, 1, n, n, n)); // normalization
const double t_end = 86400.0;
const double step = 300.0;
// Variables
int i, j; // Loop counters
double Mjd0; // Epoch (Modified Julian Date)
double t; // Integration time [s]
double max, max_Kep; // Matrix error norm
AuxParam7 Aux1 = new AuxParam7(), Aux2 = new AuxParam7(); // Auxiliary parameter records
// Model parameters for reference solution (full 10x10 gravity model) and
// simplified variational equations
// Epoch state and transition matrix
Mjd0 = OrbitConsts.MJD_J2000;
Aux1.Mjd_0 = Mjd0; // Reference epoch
Aux1.n_a = 10; // Degree of gravity field for trajectory computation
Aux1.m_a = 10; // Order of gravity field for trajectory computation
Aux1.n_G = 10; // Degree of gravity field for variational equations
Aux1.m_G = 10; // Order of gravity field for variational equations
Aux2.Mjd_0 = Mjd0; // Reference epoch
Aux2.n_a = 2; // Degree of gravity field for trajectory computation
Aux2.m_a = 0; // Order of gravity field for trajectory computation
Aux2.n_G = 2; // Degree of gravity field for variational equations
Aux2.m_G = 0; // Order of gravity field for variational equations
DeIntegrator Int1 = new DeIntegrator(VarEqn, 42, Aux1); // Object for integrating the variat. eqns.
DeIntegrator Int2 = new DeIntegrator(VarEqn, 42, Aux2); //
Geo.Algorithm.Vector y0 = new Geo.Algorithm.Vector(6), y = new Geo.Algorithm.Vector(6); // State vector
Geo.Algorithm.Vector yPhi1 = new Geo.Algorithm.Vector(42), yPhi2 = new Geo.Algorithm.Vector(42); // State and transition matrix vector
Matrix Phi1 = new Matrix(6, 6), Phi2 = new Matrix(6, 6); // State transition matrix
Matrix Phi_Kep = new Matrix(6, 6); // State transition matrix (Keplerian)
y0 = Kepler.State(OrbitConsts.GM_Earth, new Geo.Algorithm.Vector(a, e, inc, 0.0, 0.0, 0.0));
for (i = 0; i <= 5; i++)
{
yPhi1[i] = y0[i];
for (j = 0; j <= 5; j++)
{
yPhi1[6 * (j + 1) + i] = (i == j ? 1 : 0);
}
}
yPhi2 = new Geo.Algorithm.Vector(yPhi1);
// Initialization
t = 0.0;
Int1.Init(t, relerr, abserr);
Int2.Init(t, relerr, abserr);
// Header
var endl = "\r\n";
var info = "Exercise 7-1: State transition matrix" + endl
+ endl
+ " Time [s] Error (J2) Error(Kep)" + endl;
// Steps
while (t < t_end)
{
// New output time
t += step;
// Integration
Int1.Integ(t, ref yPhi1); // Reference
Int2.Integ(t, ref yPhi2); // Simplified
//info= setprecision(5) + setw(12)+yPhi1 + endl;
//info= setprecision(5) + setw(12) + yPhi2 + endl;
// Extract and normalize state transition matrices
for (j = 0; j <= 5; j++)
{
Phi1.SetCol(j, yPhi1.Slice(6 * (j + 1), 6 * (j + 1) + 5));
}
for (j = 0; j <= 5; j++)
{
Phi2.SetCol(j, yPhi2.Slice(6 * (j + 1), 6 * (j + 1) + 5));
}
Phi1 = Scale * Phi1 * scale;
Phi2 = Scale * Phi2 * scale;
// Keplerian state transition matrix (normalized)
Kepler.TwoBody(OrbitConsts.GM_Earth, y0, t, ref y, ref Phi_Kep);
Phi_Kep = Scale * Phi_Kep * scale;
// Matrix error norms
max = Max(Matrix.CreateIdentity(6) - Phi1 * InvSymp(Phi2));
max_Kep = Max(Matrix.CreateIdentity(6) - Phi1 * InvSymp(Phi_Kep));
// Output
// info = String.Format( "{0, 10:F }{1, 10:F }{2, 10:F } ", t, max , max_Kep );
info = String.Format("{0, 10:F2}{1, 10:F2}{2, 12:F2}", t, max, max_Kep);
Console.WriteLine(info);
}
;
// Output
info = endl
+ "Time since epoch [s]" + endl
+ endl
+ String.Format("{0, 10:F}", t) + endl
+ endl;
Console.Write(info);
info = "State transition matrix (reference)" + endl
+ endl
+ Phi1 + endl;
Console.Write(info);
info = "J2 State transition matrix" + endl
+ endl
+ Phi2 + endl;
Console.Write(info);
info = "Keplerian State transition matrix" + endl
+ endl
+ Phi_Kep + endl;
Console.Write(info);
Console.ReadKey();
}
