# D'alembert's principle wtf?

1. Aug 31, 2006

### leright

d'alembert's principle....wtf?

So I am a dual major in EE and physics. I have never had a theoretical mechanics course or analytical mechanics course yet. I just started a feedback control systems course (which I find extremely interesting so far). I have read through the first couple chapters of the text very carefully and everything makes clear sense with the exception of d'alembert's law, which is applied copiously throughout the text and this is quite frustrating to me.

As you are all aware, d-alembert's law states that the sum of the forces on a body is zero, and the book states this is the simply an alternative way of saying Newton's second law. Now come on, how can the book make this claim with a bunch of damn EEs reading it and not justify such a statement. I can understand if the book were to apply d'alembert's law in cases where static equilibrium occurs, but the book also applies it to dynamics situations.

Newton's 2nd law says sum(F) = ma. It seems like when going from Newton's law to d'alembert's law the ma on the right was subtracted from the right and it was not subtracted from the left to yield sum(F) = 0.

There is a situation where the book finds the X(s)/F(s) transfer function of a spring/mass/damper system, and applies the seemingly ludicrous d'alembert's principle, just like every other problem in the book, which frustrates me. Now, the book claims that Newton's second law is the same as d'alembert's principle, but if you remove the imaginary inertial force the differential equation is certainly not the same.

Now, I often get the impression, especially due to the (often poor) techniques used in explaining methodology in the engineering curriculum, and due to the shoddy quality of much of the engineering and lower level literature (also, something that bothers me is the application of KVL in inductive circuits....makes NO sense), that the techniques that 'make sense' were once applied, but it was found that the model was not accurate, and then fudge factors are applied that do not make physical sense but yield the correct models, and then engineers and scientists accept it.

Also, with the application of KVL to inductive circuits, for instance, the wrong reasoning seems to yield the correct model, but people don't care that it seems to be incorrect reasoning because it works!

Someone, please set me at ease here.

2. Aug 31, 2006

### leright

ANYONE? I suppose I can see if my control systems prof has a satifying explanation, but he is an engineer...not a physicist.

3. Sep 1, 2006

### Clausius2

Welcome to the Engineering World. Engineering is not an exact science man. During your studies you will find several patches put there to make the things work, but doubtless they work. I do know it is unpleasant to make calculations based on coefficients or correlation or patches coming from experiments. But let's talk honestly, science is employable in a percentage in daily problems of engineering. Life is so much complicated, and even science gives a great background and powerful tools to us, always there is some work to do in the lab or there is some point in which you have to look for an experimental correction.

Anyway, what you cannot do is diminish engineering for not basing its result in solid pillars. Sometimes great minds are needed for cooking solutions ad hoc for a particular problem, and by the way you are using everyday things built and designed by those minds.

Last edited: Sep 1, 2006
4. Sep 1, 2006

5. Sep 1, 2006

### leright

This isn't quite the answer I was expecting, but thanks for the insight...