singular system (odesolve)

[MilchMachtMunte]

Hi!

Another odesolve problem. The system isn't stable. I am not sure if my method is how this problem should be solved.

There is a picture in the file so it should be easier for you to understand my intentions. Feel free to write in the file.

Many thanks in advance

Greetings

[AlanStevens]

It might be best to get rid of the cargo hook altogether if you want to consider it to be massless. Simply combine the springs and dampers in series - see attached (which is an approximation of course). However, it's not clear to me why you want to consider it massless. The system works ok with the cargo hook given a small mass (say 1000 or more times smaller than the load). Note: In the file you attached you solve for displacements and velocities, but you assign the results to displacements. i.e. you repeat xh, xch and xl where you should have vh, vch and vl.

Alan

[MilchMachtMunte]

Thank you.

The solution you posted is perfect for this example. But as I have to use spring caracteristics third or fourth order it won't be possible to combine them.

In terms of the mass of the cargohook: I could give it a mass like you did, it works fine here. But as I will use a spring preload this will make troubles (it accelerates very quickly as the mass is very small in comparison to the helicopter or the load -> the influence of the cargohook is there, even if the mass is very very little). This is why I want to consider it massless.
Do you see the problem with my first version?

Leander

[AlanStevens]

If you assume the net force on the cargo hook is zero, this means it moves at constant velocity, which can be precalculated using the initial values of xh, xl, vh etc. Its displacement is simply vch*t, which can also be constructed as a function of time before the main solve block. If you now solve for the remaining variables (removing Fd = Fu from the solve block) it will find solutions for times as far as tend equals 10 (say) and beyond. However, when you look at the two forces over this time you will see they are not identical. There is an inconsistency inherent in the basic assumption of forrce equality at all times.

Alan

[MilchMachtMunte]

The velocity of the cargo hook is not constant...? Even if you choose vch =1.81 so that Fu und Fd have the same value. I didn't get the point about removing Fd=Fu.
I don't have a clue about numerical calculation but shoulden't the algorithm try to find the fitting vch so the equations are true?

Thank you for your efforts.

[AlanStevens · Accepted solution]

Leander Rankwiler wrote:

The velocity of the cargo hook is not constant...?

If you set the mass of the cargo hook to zero (so gravitational force on cargo hook is zero) and then set Fu and Fd to the same value that means the net force on the cargo hook is zero. This means that its velocity is constant (there is no force with which to change its velocity) - so the assumption that Fd is the same as Fu is unrealistic. To construct a model in which the velocity of the cargo hook isn't constant you cannot have Fu and Fd the same at all times. Hence you should remove the equality of Fd and Fu within the Guven ... Odesolve block.

Alan

[MilchMachtMunte]

got the point!
thank you!