scott wrote:
>> So if you wanted to describe the motion of a complex arrangement of 
>> rigid components (e.g., a car gearbox), you'd use kinematics?
> 
> Yes, for analysis of how fast each bit spins, but that part is actually 
> very simple and well known about gearboxes.  Kinematics would be more 
> useful to design the windscreen wiper mechanism for instance, where it 
> is assumed that the motor can generate enough torque to maintain a 
> constant speed.  What the designer must consider is how the constant 
> angular velocity of the electric motor is converted to that movement you 
> see the wiper blades making.

So things like cams and eccentrics then?

>> So... the resonant modes of a effectively 1D system (a string, a 
>> gas-filled pipe, etc.) would just be harmonics of the main resonant 
>> frequency?
> 
> Haha I should have known this had something to do with organ pipes!  Yes 
> pretty much.

Well, it was a simple example of something I've already looked at a fair 
bit.

Where I actually heard it mentioned was in relation to "the resonant 
modes of [the air in] this room".

Presumably a 2D surface like a drum head would have quite a lot of 
possible resonant modes?

How is all this related to standing waves?

>> Heh. So you know how an ideal gas is different from a real gas then? ;-)
> 
>  From what I recall, ideal gasses are ones that follow the PV=nRT 
> equation and a host of other equations.  Which works pretty well for 
> most "normal" gasses at "normal" temperature and pressure.  IIRC it 
> doesn't work for steam though, which is why we needed hideous fold-out 
> tables and charts.

...because steam can condense? (Or at least is likely to under typical 
conditions, whereas air isn't.)

>> If I take a piece of paper and hold it horisontal, it flops under its 
>> own weight. But if I fold it down the middle, now it *can* stand up 
>> under its own weight. (But only if you hold it the right way.)
> 
> You can do that without folding it too, along the edge that you are 
> holding it, just push down in the middle with your thumb above the paper 
> with two fingers underneath either side.  By introducing that slight 
> curvature in the paper you are making it very difficult to bend 
> downwards without stretching or ripping the paper, so of course then the 
> paper does not have enough weight to do that by itself.  I don't know 
> what category this would come under, dynamics or thin bodies or 
> something ;-)

Ah yes - just curving the paper makes it behave quite differently. (See 
corrigated sheet metal.) But why, I wonder?

Similarly, a hollow tube responds differently to a solid rod. And again, 
a tear tends to propogate along a sheet, but if you put a hole in the 
sheet, it actually stops the tear. WTF?

>> At the same time, a straight metal rod is very strong, but once bent 
>> it becomes drastically weaker,
> 
> Actually it usually becomes stronger after the 1st bend because you have 
> work hardened it at that point.
> 
>> and it seems that nothing will restore it to its original condition.
> 
> Because when you try to bend it back, it just wants to bend at a 
> different point rather than where the original bend was, because that 
> point is now stronger!  Eventually of course if you repeatedly bend it 
> enough fatigue will set in and it will break.

Really? OK, well that's even weirder!

Presumably there's some molecular-level *reason* for all of this?

>> Wait - there's a way to *solve* differential equations?? o_O
> 
> Use Laplace transforms, makes things way easier for non-trivial 
> differential equations.

...because the Laplace transform turns differential equations into 
algebraic equations?

Presumably there are still equations which can't be "solved" in this way 
though? (It seems quite easy to come up with a set of equations which 
yield absurdly complicated behaviour...)

>> OMG, the first time I watched this on TV, I killed myself laughing. 
>> All those hours to build, and it ****ed itself to pieces in seconds! :-D
> 
> Hehe yeh I love that program.

Did you see Scrappy Races, where the same guy tried to "tune" a 6 L 
diesel engine, and the govener fell off? (I don't know what a govener 
is, but it sounds important...)

> Our robot almost did the same, when I 
> disconnected the control interface to the PC while the motor that lifted 
> the arm was still running.  Of course it was in software that the motor 
> is stopped when it hits the switch at the end of the arm's travel, so 
> with no more control input the motor continued to wind up and start 
> bending the metal arm before I could pull the power :-)  The mechanics 
> guys weren't pleased that they had to rebuilt it.

Niiiice! :-D

>> By the way... how much of the stuff you learnt do you actually *use* 
>> now anyway? ;-)
> 
> Around 10% probably, but I would imagine every job would have a slightly 
> different 10% so I certainly don't regret doing such a wide range of 
> subjects within Engineering.

Mmm, true...

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