Model a Triple Pendulum: Step-by-Step Guide

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The discussion focuses on modeling a triple pendulum using a system of equations. The user successfully modeled single and double pendulums but struggles with the complexity of the triple pendulum's equations of motion. They provided an initial equation but expressed uncertainty about its completeness. The user seeks assistance in setting up the equations, particularly for a 2D model, which they believe can effectively demonstrate chaotic behavior.

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  • Understanding of classical mechanics principles, particularly Newton's laws of motion.
  • Familiarity with mathematical modeling techniques for dynamic systems.
  • Knowledge of chaotic systems and their characteristics.
  • Basic proficiency in using mathematical software for simulations, such as MATLAB or Python.
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  • Research the derivation of equations of motion for a triple pendulum in 2D.
  • Learn about Lagrangian mechanics as a method for modeling complex systems.
  • Explore numerical methods for simulating chaotic systems using Python or MATLAB.
  • Study the behavior of multi-body systems in classical mechanics to understand interactions.
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Students and professionals in physics, mechanical engineering, and applied mathematics who are interested in modeling dynamic systems and exploring chaotic behavior in pendulum systems.

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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.:frown:

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
 
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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.
 
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?
 
Physics Monkey said:
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.
 

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