Differential forms in Mechanical Eng.

[rdt2]

The language of differential forms is creeping into the textbooks on nonlinear continuum mechanics, replacing traditional vector mechanics. I've been struggling to come to terms with this. There's a thread in the 'Tensor Analysis and D.G' forum, where the contributors are mainly physicists or mathematicians. Are there any mechanical engineers here who have adopted this machinery and, if so, was it worth the effort?

 

[Clausius2]

The language of differential forms is creeping into the textbooks on nonlinear continuum mechanics, replacing traditional vector mechanics. I've been struggling to come to terms with this. There's a thread in the 'Tensor Analysis and D.G' forum, where the contributors are mainly physicists or mathematicians. Are there any mechanical engineers here who have adopted this machinery and, if so, was it worth the effort?

Differential forms are stronlgly valuable in nonlinear continuum mechanics. As far as I know for instance in Fluid Mechanics the differential and tensorial notation makes easier the comprehension and formulation.

Maybe usual Mechanical engineers doesn't need this skill when working at an enterprise or so. But if you plan to research in some deep topic of such field, take some time to understand it as soon as possible.

 

[Clausius2]

Although once I visited your personal web-page, I don't believe you didn't know what I said yet before.

 

[rdt2]

No problem, Clausius. My aim is to give students a grounding that will enable them to keep up with likely developments over the next 20 years (by which time I hope to be running a tapas bar in Barcelona). That means trying to predict what major changes will take place in engineering analysis over that time. The growing use of differential geometry as the most appropriate framework for deformation mechanics appears to be just such a change and so I'm putting a toe in the water. The opinion of anyone who is interested is welcome.

 

[Clausius2]

(by which time I hope to be running a tapas bar in Barcelona).

You are not going to earn any money unless you sucess in change the costumes of Barcelona inhabbitants. You must know in that city there is no "tapas culture". When you drink a beer in a bar the waiter never gives you a "tapa" with it, unless you pay for it. A "tapa" is an special event.

On the other hand, in Madrid there are a lot of places where people go for "tapas" while drinking a beer or wine. Here the "tapa" is free, the waiter always gives you one with your drink (despites the fool tourist face you have ). If you want to earn money with a "tapas bar" put it here and you'll have several profits only by selling the drink, because Madrid people is able to acknowledge a good place which gives us a good drink with a good free complement.

That's a bit out of the aim of this thread, isn't it?

 

[Rev Prez]

From an EE student's perspective--a personal one at that--I found that the trade off in using diff forms to bridge 6.013 was a steeper learning curve than what we faced in first year EM (where you had the benefit of meeting vector mechanics in calc and physics simultaneously. But what I can put quantifiably is my understanding of vector calc atrophied a lot faster before I encountered linear algebra and diff forms. I'm not sure if any other EE undergrads had similar experiences, let alone undergrads or grads in other departments. I wonder if its the same with learning Lagrangian and Hamiltonian formalism, are these good examples of how grasping a more general tool set extends the lifespan on your usable knowledge?

Rev Prez