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Puzzle 4

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zekeman

zekeman

Mechanical
Aug 30, 2004
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Defyiing law of angular momentum?

Here is a fun puzzle for you purists.

How is it that a kid sitting on a swing starting at rest can, without any help, always cause the swing to oscillate?

Please explain.
 
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I don't work for the current owners of ADAMS (could have, if I'd said yes to that call from their then Pres all those years ago), but I can say that it's a great toy.

Connecting ODEs and DAEs in a causal fashion is difficult and prone to errors. Softwares like ADAMS are acausal, so the response you get isn't always what you expect. It's normally much more interesting than what you'd expected. If your firm has a real need for 3D multi-body dynamics, get in there.


- Steve
 
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"impact dynamics"?

A hard problem for all dynamic solvers. I used a function that I coined "atanlash" for my ADAMS work. Arctangents are like step functions, only they are continuous in all differentials - something that ODE solvers like.

- Steve
 
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Very fancy stuff Greg,

Where is the proof that supports that "solution".
?
And if one exists, then what respectable journal has published it
 
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is the original question "how does something initally stationary become moving ?"

energy (= work) is added to the system (boy on a swing) by the boy moving his legs (changing the inertia of the system and adding torque to the system). in-phase additions augment.

personally, the kids got bored with swings when they found they had to do some work, much preferred the thumb-based "fun" ... it's a different world.
 
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It's actually an old competitor to ADAMS called Working Model 3d. As in all software it does some things better and some things worse than ADAMS, generally it is more fun and less customizable. I imagine it is less accurate, but the less time you spend fighting the tool, the more time you can spend modelling. MSC bought it and killed it.

Zekeman -there's no proof, that is just a full physics model of a possible solution. That is, if you built what I modelled in the real world I would expect it to behave in a roughly similar fashion. And if it didn't then I would get very interested. It may not be a good model of how a real person swings, it is a model of a mechanism that exhibits swing-like behaviour.

Notice that it takes a long time to build up a respectable amplitude - if after a minute of swinging the swing was only moving by a couple few degrees the average child would give up. Therefore the REAL method you use to start swinging is different to this, but it does confirm the point that driving a resonant system at its resonant frequency, especially with the addition of even small non linearities (in this case geometry), allows energy to be put into the system.

fex32 Yes, collisions and contact are modelled in both ADAMS and WM3D. Analytically it is a pretty horrible problem, to get realistic behaviour it is often necessary to fine tune some pretty arbitrary numbers. Here's a contact model, of one of those big container gantries smacking into an obstruction on one rail. There's some pretty neat stuff going on inside that model, I think it is one of the best 'simple' models I've done.







Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight
 
 http://files.engineering.com/getfile.aspx?folder=4b060036-6e01-4237-aa52-2033392b7fd6&file=crane.zip
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I wonder if replacing the rigid chain by a series of links makes a difference?
Click to expand...

Yes, it would make a big difference! With a rigid rod we can apply a torque to the rod, which results in a horizontal force at the pivot, which is transmitted to the ground, and that gives us the required horizontal reaction to get a horizontal accelleration at the swing.

Now consider a weightless rope, with zero flexural stiffness, hanging exactly vertical in a vacuum.

Look at the free body diagram of the would be swinger and the swing from the level of the position of the hands on the rope downwards. Because no moment can be transmitted up the rope, the centre of gravity of the swinger + swing (+ breathing apparatus) will remain exactly below the position of the hands on the rope, whatever the swinger does. Similarly this point will remain exactly below the swing pivot point. The swinger can kick legs and lean back to his or her hearts content, there can be no accelleration of the centre of gravity, because there is zero horizontal reaction force.

Of course in reality the rope is not weightless or zero stiffness, and (probably most importantly) there is air resistance to provide some reaction, so a swing can get started, but it is much more difficult than when you start with a small initial movement.

Doug Jenkins
Interactive Design Services
 
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"Zekeman -there's no proof, that is just a full physics model of a possible solution. That is, if you built what I modelled in the real world I would expect it to behave in a roughly similar fashion. And if it didn't then I would get very interested. It may not be a good model of how a real person swings, it is a model of a mechanism that exhibits swing-like behaviour."

Greg,

This is NOT physics.
It' star wars.

Without proof this is pure conjecture.

I wish somebody could show me how you could get the first increment of motion from rest. Energy alone won't do it.
Prove to me that throwing out your legs or moving your body will result in sustained motion.
If, at the start, you conserve linear horizontal momentum, there is zero motion of the CM.
Yes, or No?
 
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I wish somebody could show me how you could get the first increment of motion from rest. Energy alone won't do it.Prove to me that throwing out your legs or moving your body will result in sustained motion.If, at the start, you conserve linear horizontal momentum, there is zero motion of the CM. Yes, or No?
Click to expand...


Didn't some old Greek bloke say something about being able to move the Earth, given a fulcrum and a lever?

In answer to your question:
If you have a rigid rod: no*
If you have a flexible rope or chain: yes

*or to be more precise, yes but the Earth is included in your system, so you can increase the angular momentum of the swing by reducing the angular momentum of the Earth.

Doug Jenkins
Interactive Design Services
 
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I think we're still one step short here. I'm inclined to echo Zekeman's most recent question about how things go from full rest to the first (infinitesimal) bit of motion.

IDS, I'm not sure I can get on board with the idea that there's a difference between a flexible member vs. a rigid member. I read your post above, but I think that flexible vs. rigid makes no difference. Here's my thinking: any moment applied to the rigid member is only internalized inside the member. The moment is high at the bottom of the member, but zero at the top joint. Assuming there is a frictionless joint at the top, the net reaction is still only downwards -- i.e., no horizontal motion applied to the joint.

Engineering is not the science behind building. It is the science behind not building.
 
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EngineerTex - a rigid rod pinned at the top and pinned at the position of your hands would act the same as a flexible rope, but if you have a rod pinned at one end only you can apply a moment to it and this will create a constant shear force between the top of your hand and the pivot point.

Doug Jenkins
Interactive Design Services
 
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