Double Pendulum returning nan results. Why?

Question

When I run this code the double pendulum shows for a split second and then disappears. It seems most of the variables in the formula, num1, num2, etc., start returning nan after that split second when the pendulum disappears. Can anyone see why? I thought it had to do with converting degrees to radians at 180 degrees so I added the if statement in my convert function.

Here is the link to the Double Pendulum motion formula. I broke down the formula into pieces for simplicity's sake. https://www.myphysicslab.com/pendulum/double-pendulum-en.html

This idea came from Coding Train's Double Pendulum video: https://www.youtube.com/watch?v=uWzPe_S-RVE

#undef __STRICT_ANSI__
#include "window.h"
#include <SFML/Graphics.hpp>
#include <GL/glew.h>
#include <cmath>
#include <iostream>

namespace Window
{
    sf::ContextSettings settings;

    sf::RenderWindow window(sf::VideoMode(600, 600), "Window", sf::Style::Close | sf::Style::Titlebar, settings);

    void init()
    {
        settings.depthBits = 24;
        settings.majorVersion = 4;
        settings.minorVersion = 6;  //OpenGL 4.6

        glewInit();
        glViewport(0,0, 600, 600);
    }

    void close()
    {
        window.close();
    }

    void update()
    {
        window.display();
    }

    void checkForClose()
    {
        sf::Event windowEvent;
        while (window.pollEvent(windowEvent))
        {
            if (windowEvent.type == sf::Event::Closed)
            {
                close();
            }
        }
    }

    bool isOpen()
    {
        return window.isOpen();
    }

    double convDeg(double deg)
    {
        if (deg == 180.0)
        {
            return 0.0;
        }

        else
        {
            return deg * M_PI / 180.0;
        }
    }

    void runLoop()
    {
        double r1 = 100;
        double m1 = 40;
        double a1 = 90;
        double a1_v = 0;

        double r2 = 100;
        double m2 = 40;
        double a2 = 30;
        double a2_v = 0;

        double x1 = 0;
        double x2 = 0;
        double y1 = 0;
        double y2 = 0;

        double g = 0.005;

        double num1 = 0;
        double num2 = 0;
        double num3 = 0;
        double num4 = 0;
        double den = 0;

        double a1_a = 0;
        double a2_a = 0;

        while (window.isOpen())
        {
            num1 = -g * (2 * m1 + m2) * std::sin(convDeg(a1));
            num2 = -m2 * g * std::sin(convDeg(a1-2*a2));
            num3 = -2*std::sin(convDeg(a1-a2))*m2;
            num4 = a2_v*a2_v*r2+a1_v*a1_v*r1*std::cos(convDeg(a1-a2));
            den = r1 * (2*m1+m2-m2*cos(convDeg(2*a1-2*a2)));
            a1_a = (num1 + num2 + num3*num4) / den;

            num1 = 2 * std::sin(convDeg(a1-a2));
            num2 = (a1_v*a1_v*r1*(m1+m2));
            num3 = g * (m1 + m2) * std::cos(convDeg(a1));
            num4 = a2_v*a2_v*r2*m2*std::cos(convDeg(a1-a2));
            den = r2 * (2*m1+m2-m2*std::cos(convDeg(2*a1-2*a2)));
            a2_a = (num1*(num2+num3+num4)) / den;

            x1 = 300 + (r1 * std::sin((convDeg(a1))));
            y1 = 300 + (r1 * std::cos((convDeg(a1))));
            x2 = x1 + (r2 * std::sin((convDeg(a2))));
            y2 = y1 + (r2 * std::cos((convDeg(a2))));

            a1_v += a1_a;
            a2_v += a2_a;
            a1 += a1_v;
            a2 += a2_v;

            sf::Vertex pOne[] =
            {
                sf::Vertex(sf::Vector2f(300,300)),
                sf::Vertex(sf::Vector2f(x1,y1)),
            };

            sf::Vertex pTwo[] =
            {
                sf::Vertex(sf::Vector2f(x1,y1)),
                sf::Vertex(sf::Vector2f(x2,y2)),
            };

            window.clear();
            window.draw(pOne, 2, sf::Lines);
            window.draw(pTwo, 2, sf::Lines);

            update();
            checkForClose();

            std::cout << std::sin(convDeg(a1)) << "\n";

        }
    }
}

Answer 1

List of problems:

• convDeg: 180 and 0 degrees are not equivalent.
• Angular variables: acceleration / velocity a1_a, a1_v etc are in radians, whereas your angle variables a1, a2 etc are in degrees. Every time the loop runs, your code wrongly converts degrees into radians. Do the conversion before the main loop.
• (Speculation based on a previous answer - I could be wrong) The formulas on MyPhysicsLab seem to contradict those from other sources, e.g. here and here; a quick calculation using Lagrangian mechanics agrees with these two sources and not MPL.