/* 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 <boost/array.hpp> #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 boost::array< point_type , n > container_type; typedef boost::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 */