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/* Boost libs/numeric/odeint/examples/solar_system.cpp
Copyright 2010-2012 Karsten Ahnert
Copyright 2011 Mario Mulansky
Solar system example for Hamiltonian stepper
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or
copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#include <iostream>
#include <array>
#include <boost/numeric/odeint.hpp>
#include "point_type.hpp"
//[ container_type_definition
// we simulate 5 planets and the sun
const size_t n = 6;
typedef point< double , 3 > point_type;
typedef std::array< point_type , n > container_type;
typedef std::array< double , n > mass_type;
//]
//[ coordinate_function
const double gravitational_constant = 2.95912208286e-4;
struct solar_system_coor
{
const mass_type &m_masses;
solar_system_coor( const mass_type &masses ) : m_masses( masses ) { }
void operator()( const container_type &p , container_type &dqdt ) const
{
for( size_t i=0 ; i<n ; ++i )
dqdt[i] = p[i] / m_masses[i];
}
};
//]
//[ momentum_function
struct solar_system_momentum
{
const mass_type &m_masses;
solar_system_momentum( const mass_type &masses ) : m_masses( masses ) { }
void operator()( const container_type &q , container_type &dpdt ) const
{
const size_t n = q.size();
for( size_t i=0 ; i<n ; ++i )
{
dpdt[i] = 0.0;
for( size_t j=0 ; j<i ; ++j )
{
point_type diff = q[j] - q[i];
double d = abs( diff );
diff *= ( gravitational_constant * m_masses[i] * m_masses[j] / d / d / d );
dpdt[i] += diff;
dpdt[j] -= diff;
}
}
}
};
//]
//[ some_helpers
point_type center_of_mass( const container_type &x , const mass_type &m )
{
double overall_mass = 0.0;
point_type mean( 0.0 );
for( size_t i=0 ; i<x.size() ; ++i )
{
overall_mass += m[i];
mean += m[i] * x[i];
}
if( !x.empty() ) mean /= overall_mass;
return mean;
}
double energy( const container_type &q , const container_type &p , const mass_type &masses )
{
const size_t n = q.size();
double en = 0.0;
for( size_t i=0 ; i<n ; ++i )
{
en += 0.5 * norm( p[i] ) / masses[i];
for( size_t j=0 ; j<i ; ++j )
{
double diff = abs( q[i] - q[j] );
en -= gravitational_constant * masses[j] * masses[i] / diff;
}
}
return en;
}
//]
//[ streaming_observer
struct streaming_observer
{
std::ostream& m_out;
streaming_observer( std::ostream &out ) : m_out( out ) { }
template< class State >
void operator()( const State &x , double t ) const
{
container_type &q = x.first;
m_out << t;
for( size_t i=0 ; i<q.size() ; ++i ) m_out << "\t" << q[i];
m_out << "\n";
}
};
//]
int main( int argc , char **argv )
{
using namespace std;
using namespace boost::numeric::odeint;
mass_type masses = {{
1.00000597682 , // sun
0.000954786104043 , // jupiter
0.000285583733151 , // saturn
0.0000437273164546 , // uranus
0.0000517759138449 , // neptune
1.0 / ( 1.3e8 ) // pluto
}};
container_type q = {{
point_type( 0.0 , 0.0 , 0.0 ) , // sun
point_type( -3.5023653 , -3.8169847 , -1.5507963 ) , // jupiter
point_type( 9.0755314 , -3.0458353 , -1.6483708 ) , // saturn
point_type( 8.3101420 , -16.2901086 , -7.2521278 ) , // uranus
point_type( 11.4707666 , -25.7294829 , -10.8169456 ) , // neptune
point_type( -15.5387357 , -25.2225594 , -3.1902382 ) // pluto
}};
container_type p = {{
point_type( 0.0 , 0.0 , 0.0 ) , // sun
point_type( 0.00565429 , -0.00412490 , -0.00190589 ) , // jupiter
point_type( 0.00168318 , 0.00483525 , 0.00192462 ) , // saturn
point_type( 0.00354178 , 0.00137102 , 0.00055029 ) , // uranus
point_type( 0.00288930 , 0.00114527 , 0.00039677 ) , // neptune
point_type( 0.00276725 , -0.00170702 , -0.00136504 ) // pluto
}};
point_type qmean = center_of_mass( q , masses );
point_type pmean = center_of_mass( p , masses );
for( size_t i=0 ; i<n ; ++i )
{
q[i] -= qmean ;
p[i] -= pmean;
}
for( size_t i=0 ; i<n ; ++i ) p[i] *= masses[i];
//[ integration_solar_system
typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
const double dt = 100.0;
integrate_const(
stepper_type() ,
make_pair( solar_system_coor( masses ) , solar_system_momentum( masses ) ) ,
make_pair( boost::ref( q ) , boost::ref( p ) ) ,
0.0 , 200000.0 , dt , streaming_observer( cout ) );
//]
return 0;
}
/*
Plot with gnuplot:
p "solar_system.dat" u 2:4 w l,"solar_system.dat" u 5:7 w l,"solar_system.dat" u 8:10 w l,"solar_system.dat" u 11:13 w l,"solar_system.dat" u 14:16 w l,"solar_system.dat" u 17:19 w l
*/
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