How do you solve a system of 2nd order non linear DE's

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Mark 2013-10-18

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https://ww2.mathworks.cn/matlabcentral/answers/90633-how-do-you-solve-a-system-of-2nd-order-non-linear-de-s

编辑： Mark 2013-10-18

We are beginners with Matlab and have seriously no clue how we should solve our system of equations. We looked it up and we found something about ODE's, but again, no clue how to use them. We hope to find some help via the user community. We made a set of 3 equations for a Huygens clock, which are the following:

m_1*L_1^2*(θ_1 )''+m_1*L_1*g*sin〖θ_1 〗+m_1*L_1*cos〖θ_1 〗*x''=0
m_2*L_2^2*(θ_2 )''+m_2*L_2*g*sin〖θ_2 〗+m_2*L_2*cos〖θ_2 〗*x''=0
m_3*x''+2*k*x-m_1*L_1*(θ_1 )'^2-m_2*L_2*(θ_2 )'^2+m_1*L_1*(θ_1 )''+m_2*L_2*(θ_2 )''=0

m, L and k are all constants. The idea of a Huygens clock is that the pendulums will synchronize, therefore the fase should become the same or exactly the opposite. Any help is appreciated, because we are stuck with this for 3 days already.