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#include "cip.h"
#include "vector2.h"

//---- physical constants
const double Mstar     = 1.0;                   // mass of a star
const double G         = 1.00;                  // Gravity constant

//---- experimental settings
const double dT        = 1.0/256;               // temporal step
const int    N         = 4;                     // number of stars

//---- declaration of structure Matter
struct Matter
{
  Vector2 p, q, f;        // momentum, position, force
};

const int    symp_r = 2;
const double symp_k[2] = {
  +0.500000000000000,
  +0.500000000000000
};
const double symp_u[2] = {
  +0.000000000000000,
  +1.000000000000000
};

Init() ´Ø¿ô¤ÏÀ±¤Î½é´üÃͤòÀßÄꤹ¤ë¡£

//---- initialize properties of stars
void Init( Matter M[] )
{
  for( int n=0 ; n<N ; n++ ){
      // locate stars on circumference
    double ang = 2*M_PI/N*n;
    M[n].p  = Vector2( -sin(ang), cos(ang) );
    M[n].q  = Vector2(  cos(ang), sin(ang) );
  }
}

//---- calculates gravity force amoung two stars
Vector2 Interaction( Matter& M1, Matter& M2 )
{
  const Vector2 vec_r = M1.q - M2.q;
  const double  r     = abs(vec_r);
  return( -G*Mstar*Mstar/(r*r*r) * vec_r );
}

//---- calculates gravity field
void CalcField( Matter M[] )
{
  int n1, n2;
    // reset M[].f
  for( n1=0 ; n1<N ; n1++ ){
    M[n1].f = Vector2( 0.0, 0.0 );
  }
    // sums up M[].f
  for( n1=0 ; n1<N ; n1++ ){
    for( n2=n1+1 ; n2<N ; n2++ ){
      Vector2 f = Interaction( M[n1], M[n2] );
      M[n1].f += f;
      M[n2].f -= f;  // Newton's law "The third law of motion"
    }
  }
}

//---- calculates total energy
double CalcEnergy( Matter M[] )
{
  int n1, n2;
  double E;
    // sums up energy
  for( n1=0, E=0.0 ; n1<N ; n1++ ){
    E += (1.0/(2*Mstar))*abs2(M[n1].p);  // Kinetic Energy
    for( n2=n1+1 ; n2<N ; n2++ ){
      E += -G*Mstar*Mstar/abs(M[n1].q-M[n2].q); // Potential Energy
    }
  }
  return( E );
}

//---- main function
int main( void )
{
  int n;
  Matter M[N];
  Init( M );
  for( double T=0.0 ; T<10.0 ; T += dT ){
      // symplectic steps
    for( int r=0 ; r<symp_r ; r++ ){
      CalcField( M );
      for( n=0 ; n<N ; n++ ){         // Potential term
        M[n].p += dT*symp_u[r] * M[n].f;
      }
      for( n=0 ; n<N ; n++ ){         // Kinetic term
        M[n].q += dT*symp_k[r] * (1.0/Mstar) * M[n].p;
      }
    }
    printf("%lf %lf\n", T, CalcEnergy(M) );
  }

  return(0);
}

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//---- physical constants
const double Mele      = 1.0;                   // mass of an electron
const double Eele      = 1.0;                   // charge of an electron
const double Aint      = 1.0;                   // coupling constant of ele-ele interaction
const double Bext      = 2.0;                   // external magnetic field
const double Omega     = Eele*Bext/Mele;        // Larmor anglur frequency

//---- calculates electric force amoung two electrons
inline Vector2 Interaction( Matter& M1, Matter& M2 )
{
  const Vector2 vec_r = M1.q - M2.q;
  const double  r     = abs(vec_r);
  return( Aint*Eele*Eele/(r*r*r) * vec_r );
}

//---- calculates total energy
double CalcEnergy( Matter M[] )
{
  int n1, n2;
  double E;
    // sums up energy
  for( n1=0, E=0.0 ; n1<N ; n1++ ){
    E += 0.5/Mele*abs2(M[n1].p);                  // kinetic energy
    for( n2=n1+1 ; n2<N ; n2++ ){
      E += Aint*Eele*Eele/abs(M[n1].q-M[n2].q);   // potential energy
    }
  }
  return( E );
}

//---- main function
int main( void )
{
  int n;
  Matter M[N];
  Init( M );
  for( double T=0.0 ; T<500.0 ; T += dT ){
    for( int r=0 ; r<symp_r ; r++ ){
      CalcField( M );
      for( int n=0 ; n<N ; n++ ){     // potential term
        M[n].p += dT*symp_u[r] * M[n].f;
      }
      for( n=0 ; n<N ; n++ ){         // kinetic and Magnetic term
        double co = cos(Omega*dT*symp_k[r]);
        double si = sin(Omega*dT*symp_k[r]);
	  
        M[n].q.x += (1.0/(Mele*Omega))*( M[n].p.x*si - M[n].p.y*(1-co) );
        M[n].q.y += (1.0/(Mele*Omega))*( M[n].p.x*(1-co) + M[n].p.y*si );
        double p_x = M[n].p.x;
        M[n].p.x = p_x*co - M[n].p.y*si;
        M[n].p.y = p_x*si + M[n].p.y*co;
      }
    }
    printf("%lf %lf\n", T, CalcEnergy(M) );
  }

  return(0);
}

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