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/*
* Copyright (c) 2003 CHABBERT Jean-Philippe
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2
* as published by the Free Software Foundation.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
char geodesics_C[] = "$Header: /cvsroot/Lorene/Codes/Rot_star/Geodesics/geodesics.C,v 1.2 2014/10/06 15:12:51 j_novak Exp $" ;
/*
* $Id: geodesics.C,v 1.2 2014/10/06 15:12:51 j_novak Exp $
* $Log: geodesics.C,v $
* Revision 1.2 2014/10/06 15:12:51 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.1 2003/02/07 17:31:52 jp_chabbert
* First version with rotstar input data
*
*
*
*
* $Header: /cvsroot/Lorene/Codes/Rot_star/Geodesics/geodesics.C,v 1.2 2014/10/06 15:12:51 j_novak Exp $
*
*/
// C++ headers
// C headers
#include <cstdio>
#include <cmath>
// Lorene headers
#include "etoile.h"
#include "main.h"
void geodesics( double x, double *y, double *dydx , const Etoile_rot& star )
/* Null geodesics equations in RNS metric */
/* re = rayon de l'toile */
{
/* coordonnes et leurs drives */
double t,r,theta,phi,tp,rp,thetap,phip,tpp,rpp,thetapp,phipp;
/* Potentiels */
double alpha,rho,gamma,omega;
/* Drives des potentiels */
double dalphadr,drhodr,dgammadr,domegadr;
double dalphadtheta,drhodtheta,dgammadtheta,domegadtheta;
point p;
#ifdef DEBUG
printf("Entre dans geodesics ... ");
#endif
/* noms de variables lisibles */
t = y[1];
r = y[2];
theta = y[3];
phi = y[4];
tp = y[5];
rp = y[6];
thetap= y[7];
phip = y[8];
/* Pour se ramener systme du premier ordre */
dydx[1] = tp;
dydx[2] = rp;
dydx[3] = thetap;
dydx[4] = phip;
/* chargement des coefs de la metrique */
p=interpol2(r,theta,star);
rho=p.rho;
gamma=p.gamma;
alpha=p.alpha;
omega=p.omega;
drhodr=p.drhodr;
dgammadr=p.dgammadr;
dalphadr=p.dalphadr;
domegadr=p.domegadr;
drhodtheta=p.drhodtheta;
dgammadtheta=p.dgammadtheta;
dalphadtheta=p.dalphadtheta;
domegadtheta=p.domegadtheta;
/* Equation en t */
tpp=-dgammadr-drhodr-dgammadtheta-drhodtheta-exp(-2.*rho)*r*r*sin(theta)*sin(theta)*(-omega*domegadr*tp*rp-omega*domegadtheta*tp*thetap+domegadr*rp*thetap+domegadtheta*thetap*phip);
/* Equation en r */
rpp=0.5*(-dgammadr*exp(gamma+rho)-drhodr*exp(gamma+rho)+2*omega*exp(gamma-rho)*r*r*sin(theta)*sin(theta)*domegadr+omega*omega*exp(gamma-rho)*r*r*sin(theta)*sin(theta)*(dgammadr-drhodr)+2*omega*omega*exp(gamma-rho)*r*sin(theta)*sin(theta))*tp*tp*exp(-2.*alpha)-exp(gamma-rho-2.*alpha)*r*sin(theta)*sin(theta)*tp*phip*(r*domegadr+omega*r*dgammadr-omega*r*drhodr+2*omega)-dalphadr*rp*rp-2.*dalphadtheta*rp*thetap+r*(1.+r*dalphadr)*thetap*thetap+0.5*exp(gamma-rho-2.*alpha)*r*sin(theta)*sin(theta)*(r*dgammadr-r*drhodr+2.)*phip*phip;
/* Equation en theta */
thetapp=0.5*(-dgammadtheta*exp(gamma+rho)-drhodtheta*exp(gamma+rho)+2*omega*exp(gamma-rho)*r*r*sin(theta)*sin(theta)*domegadtheta+omega*omega*exp(gamma-rho)*r*r*sin(theta)*sin(theta)*(dgammadtheta-drhodtheta)+2*omega*omega*exp(gamma-rho)*r*r*sin(theta)*cos(theta))*tp*tp*exp(-2.*alpha)*1/(r*r)-exp(gamma-rho-2.*alpha)*sin(theta)*tp*phip*(domegadtheta*sin(theta)+omega*sin(theta)*dgammadtheta-omega*sin(theta)*drhodtheta+2.*omega*cos(theta))+dalphadtheta*rp*rp/(r*r)-2./r*(1.+r*dalphadr)*rp*thetap-dalphadtheta*thetap*thetap+0.5*exp(gamma-rho-2*alpha)*sin(theta)*(sin(theta)*dgammadtheta-sin(theta)*drhodtheta+2.*cos(theta))*phip*phip;
/* Equation en phi */
phipp=(-2*omega*r*exp(gamma+rho)*drhodr+omega*omega*r*r*r*exp(gamma-rho)*sin(theta)*sin(theta)*domegadr+exp(gamma+rho)*domegadr*r+2*omega*exp(gamma+rho))*tp*rp/(r*exp(gamma+rho))+(-2*omega*sin(theta)*exp(gamma+rho)*drhodtheta+omega*omega*r*r*exp(gamma-rho)*sin(theta)*sin(theta)*sin(theta)*domegadtheta+exp(gamma+rho)*domegadtheta*sin(theta)+2*omega*cos(theta)*exp(gamma+rho))*tp*thetap/(sin(theta)*exp(gamma+rho))-(omega*r*r*r*sin(theta)*sin(theta)*exp(gamma-rho)*domegadr+exp(gamma+rho)*(2+r*dgammadr-r*drhodr))*rp*phip/(r*exp(gamma+rho))-(omega*r*r*sin(theta)*sin(theta)*sin(theta)*exp(gamma-rho)*domegadtheta+exp(gamma+rho)*(2*cos(theta)+sin(theta)*dgammadtheta-sin(theta)*drhodtheta))*thetap*phip/(sin(theta)*exp(gamma+rho));
dydx[5] = tpp;
dydx[6] = rpp;
dydx[7] = thetapp;
dydx[8] = phipp;
#ifdef DEBUG
printf("Fin de geodesics \n");
#endif
}
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