Double pendulum solution using GSL

Question

I am learning to use GSL to solve ODE. I wanted to solve double pendulum problem using GSL ODE functions. I decided to use this equations:

Answer 1

You could also use C++ with odeint library if you are interested. For the double pendulum system. For matrices I use Eigen and for solving ODEs I use odeint , therefore this is the code for your problem.

#include 
#include 
#include 
#include 
#include 
#include 

using namespace std;
using namespace boost::numeric::odeint;


typedef std::vector< double > state_type;


void equations(const state_type &y, state_type &dy, double x)
{
    const double m1(0.5), m2(0.5),
                 L1(0.1), L2(0.1),
                 g(9.81);

    Eigen::MatrixXd M(2, 2), C(2, 1), B(2,1);

    /*
      Theta 1 =  y[0]
     dTheta 1 =  y[1] = dy[0]
    ddTheta 1 = dy[1]

      Theta 2 =  y[2]
     dTheta 2 =  y[3] = dy[2]
    ddTheta 2 = dy[3]
    */
    double delta(y[0] - y[2]);

    M <<      (m1 + m2)*L1, m2*L2*cos(delta),
          m2*L1*cos(delta),            m2*L2;


    C <<  m2*L1*L2*y[3]*y[3]*sin(delta) + g*(m1 + m2)*sin(y[0]),
         -m2*L1*y[1]*y[1]*sin(delta)    +        m2*g*sin(y[2]);


    //#####################( ODE Equations )################################
    dy[0] = y[1];
    dy[2] = y[3];

    B = M.inverse() * (-C);


    dy[1] = B(0,0);
    dy[3] = B(1,0);

}


int main(int argc, char **argv)
{
    const double dt = 0.01;
    runge_kutta_dopri5 < state_type > stepper;
    double pi = boost::math::constants::pi();

    state_type y(4); 
    // initial values
    y[0] = pi/3.0;  //  Theta 1 
    y[1] = 0.0;     // dTheta 1
    y[2] = pi/4.0; //   Theta 2
    y[3] = 0.0;    //  dTheta 2

    for (double t(0.0); t <= 5; t += dt){

        cout << fixed << setprecision(2);
        std::cout << "t: " << t << "  Theta 1: " << y[0] << "   dTheta 1: " << y[1]
                  << "  Theta 2: " << y[2] << "  dTheta 2: " << y[3] << std::endl;


        stepper.do_step(equations, y, t, dt);
    }

}

The results are