I am working on a project to write a paper on the stability of a double pendulum. The only problem is that we never covered anything that could cover a system of two second order nonlinear ODEs (taylor expansion and a little of perturbation, to make phase planes). My professor suggested(Based on the wolfram site) that I analyze the energy of the system, so I have picked up some graduate textbooks on mechanics to try and learn this.

So, I ask you if there is anything specific you can tell me to look into to be able to provide some analysis of this system for my paper.

This the system, in the form of 4 first order equations:

```
deq1 := diff(v1(t), t) = (2*sin(a1(t))*m1*g+m2*g*sin(a1(t)-2*a2(t))+sin(a1(t))*m2*g+m2*v1(t)^2*L1*sin(-2*a2(t)+2*a1(t))+2*m2*v2(t)^2*L2*sin(a1(t)-a2(t)))/(-2*L1*m1-L1*m2+L1*m2*cos(-2*a2(t)+2*a1(t)))
deq2 := diff(a1(t), t) = v1(t)
deq3 := diff(v2(t), t) = (-2*v1(t)^2*L1*m1*sin(a1(t)-a2(t))-m2*v2(t)^2*L2*sin(-2*a2(t)+2*a1(t))-m2*g*sin(-a2(t)+2*a1(t))+sin(a2(t))*g*m1-m1*g*sin(-a2(t)+2*a1(t))+sin(a2(t))*g*m2-2*m2*v1(t)^2*L1*sin(a1(t)-a2(t)))/(-2*L2*m1-L2*m2+L2*m2*cos(-2*a2(t)+2*a1(t)))
deq4 := diff(a2(t), t) = v2(t)
```