Solve Boom Crane Position with Lagrangian Equation | Wind Loading Included

In summary, the conversation discusses the modeling of a suspended mass at the end of a boom crane, which is a spherical pendulum that is affected by wind loading and controlled by a human operator. Different approaches, such as using the Lagrangian equation and representing the boom arm as a double spherical pendulum, are considered. However, the predictability of the motion of the suspended mass is questioned due to the various influences acting on it.
  • #1
volican
41
0
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.
 
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  • #2
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
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.
 

FAQ: Solve Boom Crane Position with Lagrangian Equation | Wind Loading Included

1. What is a Lagrangian equation and how is it used to solve for boom crane positions?

A Lagrangian equation is a mathematical formula that is used to model the motion of a system based on its kinetic and potential energy. In the context of solving for boom crane positions, the Lagrangian equation is used to determine the position of the crane by taking into account the forces acting on it, such as the weight of the boom and the wind loading. It allows for a more accurate and comprehensive analysis of the crane's motion compared to simpler equations.

2. How does wind loading affect the position of a boom crane?

Wind loading is a significant factor to consider when determining the position of a boom crane. The force of the wind can cause the crane to sway or tip, depending on its direction and strength. This can affect the stability and safety of the crane, and therefore it must be taken into account when solving for its position. The Lagrangian equation allows for the inclusion of wind loading in the analysis.

3. What other factors are considered when solving for boom crane positions?

In addition to wind loading, other factors that are typically considered when solving for boom crane positions include the weight and geometry of the crane, the location and weight of the load being lifted, and the strength and direction of any other external forces acting on the crane. The Lagrangian equation allows for the incorporation of all these factors in a comprehensive analysis.

4. How accurate is the solution obtained using the Lagrangian equation?

The accuracy of the solution obtained using the Lagrangian equation depends on the accuracy of the input data and assumptions made in the analysis. It is a highly versatile equation that can yield very accurate results when used correctly. However, it is always important to verify the results through physical testing and make any necessary adjustments.

5. Are there any limitations to using the Lagrangian equation to solve for boom crane positions?

While the Lagrangian equation is a powerful tool for analyzing the motion of a system, it does have some limitations. It assumes that the system is in equilibrium, meaning that all forces are balanced and the system is not accelerating. In reality, boom cranes are constantly in motion and may experience dynamic forces that cannot be accurately modeled using the Lagrangian equation. Therefore, it is important to consider these limitations when using the equation and make necessary adjustments as needed.

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