I'm trying to create a java application that models the path of a double pendulum. To do so I have been attempting to use Lagrangian Mechanics to find the equation's of motion for the system. The problem is that I have never seen a set of equations like the one yielded by this method and need help choosing a numerical method to use to solve it. I do not have much experience with numerical methods so please be descriptive in your response. Thank you very much to anyone who reads this and or replies. The equations are(adsbygoogle = window.adsbygoogle || []).push({});

(m1 + m2) * l1 * (second derivative of θ1) + m2 * l2 * (second derivative of θ2) * cos(θ1-θ2) + m2 * l2 * (derivative of θ2)^2 * sin(θ1 - θ2) + g * (m1 + m2) * sin(θ1) = 0

m2 * l2 * (second derivative of θ1) + m2 * l1 * (second derivative of θ1) * cos(θ1 - θ2) - m2 * l1 * (derivative of θ1)^2 * sin(θ1 - θ2) + m2 * g * sin(θ2) = 0

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# Numerical method to use on a system of second order nonlinear ODE's

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