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int Satellite::satellite_number = 0;
const std::vector<double> Satellite::coef_time_step { 0.000000000000000000, 0.056262560526922147, //коэффиценты для разбития
0.180240691736892365, 0.352624717113169637, // шага на подинтервалы
0.547153626330555383, 0.734210177215410532,
double calculate_E(const double M, const double e) {
double buffer_Ek{ M };
double buffer_Ek1{ 0 };
for (short i = 0; i < 4; i++) {
//buffer_Ek1 = M + e * sin(buffer_Ek);
buffer_Ek1 = buffer_Ek - ((buffer_Ek - e*sin(buffer_Ek) - M) / (1 - e * cos(buffer_Ek)));
buffer_Ek = buffer_Ek1;
}
return buffer_Ek1;
}
m_r = sqrt(pow(DCS(0, 0), 2) + pow(DCS(1, 0), 2) + pow(DCS(2, 0), 2));
m_h = m_r - Radius_Earth * (1 - compression_earth*pow((DCS(2,0)/m_r), 2));
m_density = 2E-13 * exp((-m_h + 200) / 60);
return 0;
m_v = sqrt(pow(DVS(0, 0), 2) + pow(DVS(1, 0), 2) + pow(DVS(2, 0), 2));
Matrix& Satellite::calculate_F(const Matrix& i_DCS, const Matrix& i_DVS) {
double Sb = m_param.cross_sectional_radius / m_param.mass;
void Satellite::step_calculate_F(const Matrix& i_DCS, const Matrix& i_DVS, std::vector<Matrix>& F, const double step_time, const short step_integration)
F.at(step_integration) = m_moon->calculateFm(i_DCS, step_time) + m_sun->calculateFs(i_DCS, step_time) +
m_sun->calculatePs(i_DCS, m_param, step_time) + m_earth->recalculateAccelerationCC(step_time, i_DCS) +
calculate_F(i_DCS, i_DVS);
//F.at(step_integration) = i_DCS + step_time ;
void calc_α(std::vector<Matrix>& α,const std::vector<Matrix>& F, const std::vector<double>& step_time, int current_moment) {
α[1] = (((F[2] - F[0]) / step_time[2]) - α[0]) / (step_time[2] - step_time[1]);
α[2] = ((((F[3] - F[0]) / step_time[3]) - α[0]) /
(step_time[3] - step_time[1]) - α[1]) /
(step_time[3] - step_time[2]);
α[3] = ((((F[4] - F[0]) / step_time[4] - α[0]) /
(step_time[4] - step_time[1]) - α[1]) /
(step_time[4] - step_time[2]) - α[2]) /
(step_time[4] - step_time[3]);
α[4] = (((((F[5] - F[0]) / (step_time[5]) - α[0]) /
(step_time[5] - step_time[1]) - α[1]) /
(step_time[5] - step_time[2]) - α[2]) /
(step_time[5] - step_time[3]) - α[3]) /
(step_time[5] - step_time[4]);
α[5] = ((((((F[6] - F[0]) / step_time[6] - α[0]) /
(step_time[6] - step_time[1]) - α[1]) /
(step_time[6] - step_time[2]) - α[2]) /
(step_time[6] - step_time[3]) - α[3]) /
(step_time[6] - step_time[4]) - α[4]) /
(step_time[6] - step_time[5]);
α[6] = (((((((F[7] - F[0]) / step_time[7] - α[0]) /
(step_time[7] - step_time[1]) - α[1]) /
(step_time[7] - step_time[2]) - α[2]) /
(step_time[7] - step_time[3]) - α[3]) /
(step_time[7] - step_time[4]) - α[4]) /
(step_time[7] - step_time[5]) - α[5]) /
(step_time[7] - step_time[6]);
for (short i = 0; i < 9; i++)
m_A.push_back(Matrix{ 3, 1 });
Satellite::Satellite(double time_TDB, satellite_parameters& i_param, Matrix& i_DCS, Matrix& i_DVS,
Moon* ptr_moon, Sun* ptr_sun, Earth* ptr_earth):
m_start_time{ time_TDB },
last_moment_integration{ time_TDB },
m_param{ i_param },
m_DCS{ i_DCS },
m_DVS{ i_DVS },
m_moon{ ptr_moon },
m_sun{ ptr_sun },
m_earth{ ptr_earth },
m_Id{ satellite_number++ },
m_Keo{ 0.0,0.0,0.0,0.0,0.0,0.0 }
{
satellite_number++;
initialization_A();
calculate_r(m_DCS);
calculate_density(m_DCS);
calculate_V(m_DVS);
Satellite::Satellite(double time_MJD, satellite_parameters& i_param, Kepler_elements_orbit& i_Keo,
Moon* ptr_moon, Sun* ptr_sun, Earth* ptr_earth):
m_param{ i_param },
m_start_time{ time_MJD },
last_moment_integration{ time_MJD },
m_Keo{i_Keo},
m_moon{ ptr_moon },
m_sun{ ptr_sun },
m_earth{ ptr_earth },
m_Id{ satellite_number++ }
m_Keo.convertKeplerToDC(m_DCS, m_DVS, m_earth->gravitational_parameter_Earth);
//std::cout << std::setprecision(20)<< m_Keo << "\nStart DCS: " << m_DCS << "Start DVS: " << m_DVS;
m_Keo.convertDCtoKepler(m_DCS, m_DVS, m_earth->gravitational_parameter_Earth);
//std::cout << m_Keo;
m_r = m_Keo.get_r();
m_v = m_Keo.get_V();
int Satellite::integration_step(double end_time_integration, double step){
std::vector<double> step_time{};
std::vector<double> global_step_time{};
std::vector<Matrix> F{}; //массив хранящий ускорения по подшагам
std::vector<Matrix> A{}; //массив хранящий коэффициенты полинома
std::vector<Matrix> α{m_A}; //массив хранящий параметры коэффициентов полинома
Matrix buff_DCS{};
Matrix buff_DVS{};
Matrix coef_c{ coef_time_step.size(),coef_time_step.size() };
for (short i = 0; i < coef_time_step.size(); i++) {
step_time.push_back(step * coef_time_step.at(i));
global_step_time.push_back((end_time_integration - last_moment_integration) * coef_time_step.at(i) + last_moment_integration);
}
for (short i = 0; i < coef_time_step.size(); i++) {
for (short j = 1; j < coef_time_step.size(); j++) {
if (i == j)
coef_c(i, j) = 1;
else if (i == 0)
coef_c(j, i) = -step_time.at(j) * coef_c(j - 1, 0);
else
coef_c(i, j) = coef_c(i-1,j-1) - step_time.at(i) * coef_c(i - 1, j);
for (int i = 0; i < coef_time_step.size(); i++) {
A.push_back(Matrix{ 3, 1 });
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for (short i = 0; i < 9; i++) {
buff_DCS = m_DCS + step_time.at(i) * m_DVS +
(1.0 / 2.0) * F.at(0) * pow(step_time.at(i), 2) +
(1.0 / 6.0) * A.at(0) * pow(step_time.at(i), 3) +
(1.0 / 12.0) * A.at(1) * pow(step_time.at(i), 4) +
(1.0 / 20.0) * A.at(2) * pow(step_time.at(i), 5) +
(1.0 / 30.0) * A.at(3) * pow(step_time.at(i), 6) +
(1.0 / 42.0) * A.at(4) * pow(step_time.at(i), 7) +
(1.0 / 56.0) * A.at(5) * pow(step_time.at(i), 8) +
(1.0 / 72.0) * A.at(6) * pow(step_time.at(i), 9);
buff_DVS = m_DVS + F.at(0) * step_time.at(i) +
(1.0 / 2.0) * A.at(0) * pow(step_time.at(i), 2) +
(1.0 / 3.0) * A.at(1) * pow(step_time.at(i), 3) +
(1.0 / 4.0) * A.at(2) * pow(step_time.at(i), 4) +
(1.0 / 5.0) * A.at(3) * pow(step_time.at(i), 5) +
(1.0 / 6.0) * A.at(4) * pow(step_time.at(i), 5) +
(1.0 / 7.0) * A.at(5) * pow(step_time.at(i), 7) +
(1.0 / 8.0) * A.at(6) * pow(step_time.at(i), 8);
step_calculate_F(buff_DCS, buff_DVS, F, global_step_time.at(i), i);
calc_α(α, F, step_time, i);
A.at(0) = α.at(0) +
coef_c(1, 0) * α.at(1) +
coef_c(2, 0) * α.at(2) +
coef_c(3, 0) * α.at(3) +
coef_c(4, 0) * α.at(4) +
coef_c(5, 0) * α.at(5) +
coef_c(6, 0) * α.at(6);
A.at(1) = α.at(1) +
coef_c(2, 1) * α.at(2) +
coef_c(3, 1) * α.at(3) +
coef_c(4, 1) * α.at(4) +
coef_c(5, 1) * α.at(5) +
coef_c(6, 1) * α.at(6);
A.at(2) = α.at(2) +
coef_c(3, 2) * α.at(3) +
coef_c(4, 2) * α.at(4) +
coef_c(5, 2) * α.at(5) +
coef_c(6, 2) * α.at(6);
A.at(3) = α.at(3) +
coef_c(4, 3) * α.at(4) +
coef_c(5, 3) * α.at(5) +
coef_c(6, 3) * α.at(6);
A.at(4) = α.at(4) +
coef_c(5, 4) * α.at(5) +
coef_c(6, 4) * α.at(6);
A.at(5) = α.at(5) + coef_c(6, 5) * α.at(6);
A.at(6) = α.at(6);
m_A = α;
last_moment_integration = end_time_integration;
m_Keo.convertDCtoKepler(m_DCS, m_DVS, m_earth->gravitational_parameter_Earth);
double Kepler_elements_orbit::convertGradToRad(double grad)
{
return grad * (M_PI / 180);
}
double Kepler_elements_orbit::convertRadToGrad(double rad)
{
return rad * (180 / M_PI);
}
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int Kepler_elements_orbit::calculateConstantVectors(const Matrix& DCS, const Matrix& DVS, const double gp)
{
constantVectorAreas.at(1) = DCS(1, 0) * DVS(2, 0) - DCS(2, 0) * DVS(1, 0);
constantVectorAreas.at(2) = DCS(2, 0) * DVS(0, 0) - DCS(0, 0) * DVS(2, 0);
constantVectorAreas.at(3) = DCS(0, 0) * DVS(1, 0) - DCS(1, 0) * DVS(0, 0);
constantVectorAreas.at(0) = sqrt(constantVectorAreas.at(1) * constantVectorAreas.at(1) +
constantVectorAreas.at(2) * constantVectorAreas.at(2) +
constantVectorAreas.at(3) * constantVectorAreas.at(3));
constantVectorLaplace.at(1) = -gp * (DCS(0, 0) / r) + constantVectorAreas.at(3) * DVS(1, 0) - constantVectorAreas.at(2) * DVS(2, 0);
constantVectorLaplace.at(2) = -gp * (DCS(1, 0) / r) + constantVectorAreas.at(1) * DVS(2, 0) - constantVectorAreas.at(3) * DVS(0, 0);
constantVectorLaplace.at(3) = -gp * (DCS(2, 0) / r) + constantVectorAreas.at(2) * DVS(0, 0) - constantVectorAreas.at(1) * DVS(1, 0);
constantVectorLaplace.at(0) = sqrt(constantVectorLaplace.at(1) * constantVectorLaplace.at(1) +
constantVectorLaplace.at(2) * constantVectorLaplace.at(2) +
constantVectorLaplace.at(3) * constantVectorLaplace.at(3));
return 0;
}
int Kepler_elements_orbit::calculateAccessoryParameter(const double gp)
{
p = a * (1 - e*e); //вычисление фокального парметра
E = calculate_E(convertGradToRad(M), e); // вычисление эксцентрической аномалии
r = a * (1 - e * cos(E)); // вычисление радиус вектора до спутника
double sin_N = (sqrt(1-e*e)*sin(E)) / (1-e*cos(E));
double cos_N = (cos(E) - e) / (1 - e * cos(E));
N = atan2(sin_N, cos_N);
dN = sqrt(p * gp)/(r*r); // Вычисление первой производной от истинной аномалии
T = 2 * M_PI * sqrt(pow(a, 3) / gp);
double sin_u = sin_N * cos(convertGradToRad(ω)) + cos_N * sin(convertGradToRad(ω));
double cos_u = cos_N * cos(convertGradToRad(ω)) - sin_N * sin(convertGradToRad(ω));
u = atan2(sin_u, cos_u);
velocity.at(0) = sqrt((gp / p) * (1 + e * e + 2 * e * cos_N)); //вычисление модуля векотра скорости
velocity.at(1) = sqrt(gp / p) * e * sin_N;
velocity.at(2) = sqrt(gp / p) * (1 + e * cos_N);
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return 0;
}
int Kepler_elements_orbit::calculate_i()
{
if (constantVectorAreas.at(3) >= 0)
i = acos(abs(constantVectorAreas.at(3) / constantVectorAreas.at(0)));
else
i = M_PI - acos(abs(constantVectorAreas.at(3) / constantVectorAreas.at(0)));
return 0;
}
int Kepler_elements_orbit::calculate_Ω()
{
if ((constantVectorAreas.at(1) >= 0) && (constantVectorAreas.at(2) <= 0))
Ω = atan(abs(constantVectorAreas.at(1) / constantVectorAreas.at(2)));
else if ((constantVectorAreas.at(1) >= 0) && (constantVectorAreas.at(2) > 0))
Ω = M_PI - atan(abs(constantVectorAreas.at(1) / constantVectorAreas.at(2)));
else if ((constantVectorAreas.at(1) < 0) && (constantVectorAreas.at(2) >= 0))
Ω = M_PI + atan(abs(constantVectorAreas.at(1) / constantVectorAreas.at(2)));
else
Ω = 2*M_PI + atan(abs(constantVectorAreas.at(1) / constantVectorAreas.at(2)));
return 0;
}
int Kepler_elements_orbit::calculate_ω()
{
double buff_sin, buff_cos;
if (cos(i) != 0) {
buff_sin = (-constantVectorLaplace.at(1) * sin(Ω) + constantVectorLaplace.at(2) * cos(Ω)) /
(constantVectorLaplace.at(0) * cos(i));
buff_cos = (constantVectorLaplace.at(1) * cos(Ω) + constantVectorLaplace.at(2) * sin(Ω)) /
constantVectorLaplace.at(0);
}
else {
buff_cos = constantVectorLaplace.at(2) / (constantVectorLaplace.at(0) * sin(Ω));
buff_sin = constantVectorLaplace.at(3) / constantVectorLaplace.at(0);
}
ω = atan2(buff_sin, buff_cos);
return 0;
}
int Kepler_elements_orbit::calculate_u(const Matrix& DCS)
{
double buff_sin, buff_cos;
buff_sin = DCS(2,0) / (r * sin(i));
buff_cos = DCS(0, 0) / r * cos(Ω) + DCS(1, 0) / r * sin(Ω);
u = atan2(buff_sin, buff_cos);
return 0;
}
int Kepler_elements_orbit::calculate_N()
{
double buff_sin, buff_cos;
buff_sin = sin(u) * cos(ω) - cos(u) * sin(ω);
buff_cos = cos(u) * cos(ω) + sin(u) * sin(ω);
N = atan2(buff_sin, buff_cos);
return 0;
}
int Kepler_elements_orbit::RevereseCalculateE()
{
double buff_sin, buff_cos;
buff_sin = (sqrt(1-e*e)*sin(N)) / (1+e*cos(N));
buff_cos = (cos(N) + e) / (1 + e*cos(N));
E = N + atan2((buff_sin*cos(N) - buff_cos*sin(N)),buff_cos*cos(N) + buff_sin*sin(N));
return 0;
}
int Kepler_elements_orbit::ReverseCalculateM()
{
M = E - e * sin(E);
return 0;
}
int Kepler_elements_orbit::convertKeplerToDC(Matrix& DCS, Matrix& DVS, const double gp)
{
calculateAccessoryParameter(gp);
DCS(0, 0) = r * (cos(u) * cos(convertGradToRad(Ω)) - sin(u) * sin(convertGradToRad(Ω)) * cos(convertGradToRad(i)));
DCS(1, 0) = r * (cos(u) * sin(convertGradToRad(Ω)) + sin(u) * cos(convertGradToRad(Ω)) * cos(convertGradToRad(i)));
DCS(2, 0) = r * sin(u) * sin(convertGradToRad(i));
DVS(0, 0) = velocity.at(1) * (DCS(0, 0) / r) - (sin(u) * cos(convertGradToRad(Ω))
+ cos(u) * sin(convertGradToRad(Ω)) * cos(convertGradToRad(i))) * velocity.at(2);
DVS(1, 0) = velocity.at(1) * (DCS(1, 0) / r) - (sin(u) * sin(convertGradToRad(Ω))
- cos(convertGradToRad(Ω)) * cos(u) * cos(convertGradToRad(i))) * velocity.at(2);
DVS(2, 0) = velocity.at(1) * (DCS(2, 0) / r) + cos(u) * sin(convertGradToRad(i)) * velocity.at(2);
return 0;
}
int Kepler_elements_orbit::convertDCtoKepler(const Matrix& DCS, const Matrix& DVS, const double gp)
{
r = sqrt(DCS(0,0) * DCS(0, 0) + DCS(1, 0) * DCS(1, 0) + DCS(2, 0) * DCS(2, 0));
calculateConstantVectors(DCS, DVS, gp);
e = (constantVectorLaplace.at(0) / gp);
p = (constantVectorAreas.at(0) * constantVectorAreas.at(0)) / gp;
a = p / (1 - e * e);
calculate_i();
calculate_Ω();
calculate_ω();
calculate_u(DCS);
calculate_N();
RevereseCalculateE();
ReverseCalculateM();
return 0;
}
int Kepler_elements_orbit::setKeo(double i_a, double i_e, double i_i, double i_Ω, double i_ω, double i_M)
{
a = i_a;
e = i_e;
i = i_i;
Ω = i_Ω;
ω = i_ω;
M = i_M;
return 0;
}
std::ostream& operator<<(std::ostream& out, const Kepler_elements_orbit& keo)
{
out << "Semi-major axis = " << keo.a << "\neccentricity = " << keo.e
<< "\nthe angle of inclination of the orbit in degrees = " << keo.i
<< "\nlongitude of the ascending node in degrees = " << keo.Ω
<< "\nthe perigee argument in degrees = " << keo.ω
<< "\nthe magnitude of the average anomaly in degrees = " << keo.M << "\n";
return out;
}