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My question essentially contains two parts: one practical question and one philosophical question.

Background

I am an engineering student working in the field of Multi Body Dynamics (MBD). My current research is in the application side of Mechanics, but I've always been fascinated by the more pure side of things, appreciating the beauty of Physics (Mechanics) and Mathematics in general.

Practical Question

Current trend today in MBD is towards writing code, doing simulations for some practical problems. While gratifying, this isn't quite as satisfying as the pleasure one gets in studying pure classical/analytical mechanics. Owing to this, I am thinking of moving into classical/analytical mechanics for my further studies. However, I have some sincere doubts.

  • Research prospects in this field: since the field is so old, are there enough problems left to solve?
  • What are the current research trends? Besides the applications of existing mechanics theories in various areas, what are the research trends in the "pure" side of mechanics?
  • Should I join the Maths department? Is the actual research in the "pure" side going in the Maths department?

Philosophical Question

Let us now imagine a (hypothetical) near future where some software has been written which can simulate any mechanics problem and optimize designs perfectly. In that case, what use is a mechanician going to be?

As for me, I've been very impressed by the thoughts of Papastavridis given in his book Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems. He has put some deep, nice views on this. His view is that Analytical Mechanics is something to be pursued for its own sake, not for some end goal. This is something which I personally agree with. But this poses a practical problem of being useless to the society.

Given that finding something new in this domain is very tough and practical utility of theories being covered by the softwares, the philosophical question is essentially this : What's a mechanician to do?

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    $\begingroup$ I mean, given that how bicycles work was still an open and engaging problem in 2010, I'm sure there are research opportunities in the classical mechanics sphere. If you want something sort of in the middle between, computational fluid dynamics research like figuring out how a dragonfly flies, if its wings are evolved to be optimally efficient, etc. is very interesting in modern applied mechanics. $\endgroup$ – CR Drost Sep 30 '15 at 22:25
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    $\begingroup$ I think the philosophical part might be off-topic for Physics. $\endgroup$ – HDE 226868 Sep 30 '15 at 23:30
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    $\begingroup$ About perfect simulations, I've opined "if all you do is simulate nature as closely as possible, you have done nothing at all." Also, such simulations are impossible. I also think the "useless to society" line of thought is fundamentally flawed. If you want to worry about your future, worry about the opportunity cost (money, free time, relationships) of doing what you love, not whether there is room for you to do what you love in the first place. $\endgroup$ – user10851 Oct 1 '15 at 2:16
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Current trend today in MBD is towards writing code, doing simulations for some practical problems.

That is not entirely true and it mostly depends on the actual areas and topics you are dealing with, as for all the other subjects. Of course, due to the industrial applications, the practical side always has more money and more academic positions, but this does not mean there is no research going on for theoreticians.

Mechanics is a very broad term: there is quantum mechanics, quantum field theory, statistical mechanics, classical mechanics (foundations and mathematics), astrophysics (dealing with mechanics of clusters); everything will depend upon the area you choose and each one will have their one (more or less spread) research trends. And yes, it is plenty of problems left to be solved (especially in pure theoretical physics and mathematics); the problem might just be that pretty often Academia has very limited funds for such position, although this strongly depends on the country you want to do research in.

I have personally done research in mathematical aspects of quantum field theory and quantum gravity and it has been a lot of fun. There are a quite a few areas of pure mathematics that can directly be translated into physics, if you still like to have a side back on your previous background: I especially refer to non-commutative geometry, Lie group theory, knot theory, theory of categories and similars. If you really like it then go for it by all means, doing pure research might not be winning the lottery but, as you mentioned, it is a pleasure.

Coming to your last question again: there is no such figure as the mechanician. Most of modern theoretical physics is field theory (in all flavours); field theory is itself mechanics but evolves into many other aspects, passing through geometry, theory of operators on (some) spaces, group theory and all the rest. On the practical side if you join Academia you will work on some particular topics (that your department has funds for) which will hopefully be related to what you like, exploiting the features of classical, quantum or whatever other type of mechanics.

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