Double Pendulum with motor between segments

[soceric]

Hello everyone,

First, I must apologize in advance as I am no physicist, and am unable to be of any help in physics to anyone else at a high level. I have a general knowledge of a wide range of subjects, and I have a problem that I need to understand better. So, with that said, here is my question.

I'm interested in the concept of momentum transfer between segments of a double pendulum system. Essentially conservation of momentum.. right? One segment decelerates while the other accelerates.

First question. Does one segment give up it's momentum to the next, or does one segment draw momentum from the other. Is this just semantics?

Second question. Both segments are interacting with one another through a pivot point. One segment slows down while the next segment speeds up. Let's change the scenario though. What would happen if there was a motor between the links at the pivot point forcefully causing the angle of the joint to change. In this case how would the transfer of momentum be affected between the segments? Would it just speed up?

I know I've most likely done a hatchet job to some physics terms in writing this out, so I hope you get the gist of what I'm trying to ask, But any help would be much appreciated.

Thank You

 

[Andy Resnick]

What you are describing is a fairly complicated system- complicated because the range of possible motions and behaviors of such a system is quite vast: stable oscillations, unstable, chaotic oscillations... to name three.

To answer question 1, I don't think it's correct to divide up the system like that- the two segments do not act independently of the other (except, perhaps, as a limiting case). Rather, the total momentum is the only well-defined measure. How it is partitioned among the internal degrees of freedom, and how that varies in time, can probably be written down (most easily by working in terms of Lagrangian or Hamiltonian mechanics).

For question 2, what you describe is a phenomenon that can be modeled by 'negative friction' (Froude's pendulum). The dynamics are incredibly complex.

Does that help?

 

[Cantab Morgan]

I'm interested in the concept of momentum transfer between segments of a double pendulum system. Essentially conservation of momentum.. right? One segment decelerates while the other accelerates.

To answer question 1, I don't think it's correct to divide up the system like that- the two segments do not act independently of the other (except, perhaps, as a limiting case). Rather, the total momentum is the only well-defined measure.

soceric, perhaps you are thinking of the energy rather than momentum? If one bob is oscillating more rapidly, and then over time the other is, then could we say that the kinetic energy is transferring from one to the other?

One thing to keep in mind is that pendulums are difficult to model by conservation of momentum because there are net external forces on the pendulum. Strictly speaking, when a bob reverses direction because it's reached its peak height, the entire Earth moves (imperceptibly) to compensate.