Model a Triple Pendulum: Step-by-Step Guide

[leon1127]

I am trying to do a computer model of a triple pendulum.
I have looked up some of the models for single and double pendulum and successfully model them.
but when i start of triple pendulum, i encounter a really fundamental problem, i don't know how to write the system of equation for that.

i got the first equation to be (m1+m2+m3)[L1]^2 [x1]''+(m2+m3)([L1][L2][L3]) [x2]''+(m1+m2+m3)[L1]g [x1] ==0

but i feel that the first equation has already missing something. but i can't really tell because my mechanic class was taken long time ago and the book i have doesn't explain much about setting up the equation. it just basically told me that is the equation.

any help will be appreciated

 

[leon1127]

anyone?

I asked my TA for help and they just simply ignored me... I know this question might increase their workload.
Any 3 bodies system like 3 masses spring system also work too. i just want to understand how to setup such system.

 

[Physics Monkey]

It isn't too difficult to write down equations of motion for this system, but they will be a bit longish. Before I try to explain how to get them though, do you have in mind pendula confined to swing in a plane or free to move in all three dimensions?

 

[leon1127]

It isn't too difficult to write down equations of motion for this system, but they will be a bit longish. Before I try to explain how to get them though, do you have in mind pendula confined to swing in a plane or free to move in all three dimensions?

I am actually doing it in 2D at this time. i believe 2d can fully demotrate a chaotic system.