# I Boom Crane - Lagrangian

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1. Dec 16, 2016

### volican

Hi,

I am trying to model the position of the suspended mass at the end on a boom crane. This is basically a spherical pendulum, however further complicated by the fact that the mass can be hoisted up and down and also the pivot is connected to an arm (boom) which can be rotated up and down and left and right. I would also like to add the effect of wind loading on the mass. Several of these things can be happening at the same time.

Having done some background research I am thinking that I would be best solving this with the Lagrangian equation. Do you think this would be the best approach? I have found some worked examples to derive the equations of motion for a 2DF double pendulum and also a spherical pendulum. I am thinking that the boom arm with the string and mass attached could be represented as a double spherical pendulum, however have the angles for the boom arm different from that of the string and mass? Do you think this makes sense?

I have also found a worked example that shows a simple pendulum where the length gets shorter, I am thinking that this would represent the mass being hoisted and I plan to use the same approach in this model. For the wind loading would I be correct in thinking that this would go on the RHS of the Lagrange equation?

Any suggestions would be most welcome and appreciated.

2. Dec 18, 2016

### Nidum

These types of problem usually have no meaningful solution .

Why do you think that the motion of your suspended mass with so many different and random influences acting on it would be predictable ?

3. Dec 18, 2016

### volican

Thanks for taking the time to write back.

What makes you say that there would be no meaningful solution? Aside from the wind, the boom arm is controlled by the human operator.