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Double Pendulum Discussion
By David Lee on Monday, September 24, 2001 - 07:12 pm:

How can I model a double pendulum (a simple pendulum with a second pendulum pivoting from the centre of mass of the first)?

By Geoff Milward on Tuesday, September 25, 2001 - 01:19 pm:


The double pendulum is a problem best solved using the anaylitcal mechanics of Lagrange & Hamiltion using generalised co-ordinate systems. This is not something you usually meet until the second year of a maths / physics degree and as I am not sure of your background I cannot say which books were appropriate to look at.

Geoff

By David Lee on Wednesday, September 26, 2001 - 07:20 pm:

It's only A-level physics coursework.
I filmed double pendulums with identicle masses and the lengths in simple ratios, starting with small initial angles. The data I got (every two frames [2/25seconds]) for the angle about the fixed point oscillates with two superposed frequencys...
I was hoping I could relate this data to some theory.

By Geoff Milward on Friday, September 28, 2001 - 12:55 pm:

For small angles I guess you can simplify things a lot. As I recall the behaviour at larger angles cannot be integrated.

Geoff

By Brad Rodgers on Friday, September 28, 2001 - 08:49 pm:

Here is a simulation of a double pendulum. I'd be interested on how it works, because my guess would be it uses piecewise approximations of differential equations- differential equations that would be very useful in solving this problem.