PowSwingByInv.cpp

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 *   Copyright (C) 2004-2015 The PaGMO development team,                     *
 *   Advanced Concepts Team (ACT), European Space Agency (ESA)               *
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#include "PowSwingByInv.h"
#include <math.h>

void PowSwingByInv (const double Vin,const double Vout,const double alpha,
                                        double &DV,double &rp)
{
        const int maxiter = 30;
        int i = 0;
        double err = 1.0;
        double f,df;                    // function and its derivative
        double rp_new;
        const double tolerance = 1e-8;

        double aIN  = 1.0/pow(Vin,2);     // semimajor axis of the incoming hyperbola
        double aOUT = 1.0/pow(Vout,2);    // semimajor axis of the incoming hyperbola

        rp = 1.0;
        while ((err > tolerance)&&(i < maxiter))
        {
                i++;
                f = asin(aIN/(aIN + rp)) + asin(aOUT/(aOUT + rp)) - alpha;
                df = -aIN/sqrt((rp + 2 * aIN) * rp)/(aIN+rp) -
                         aOUT/sqrt((rp + 2 * aOUT) * rp)/(aOUT+rp);
                rp_new = rp - f/df;
                if (rp_new > 0)
                {
                        err = fabs(rp_new - rp);
                        rp = rp_new;
                }
                else
                        rp /= 2.0;
        }

        // Evaluation of the DV
        DV = fabs (sqrt(Vout*Vout + (2.0/rp)) - sqrt(Vin*Vin + (2.0/rp)));
}