Why Do First-Year Grad Students Take Classical Mechanics?

[morangta]

Why do first-year grad students take classical mechanics, besides those wanting to analyze mechanical systems?

This would be a course along the lines of Goldstein, etc.

Do some of the concepts/methods show up later in quantum mechanics, nuclear physics?

If they skipped this mechanics course, would they not understand the material as well in these two latter topics of study?

 

[negru]

there's lots of stuff in an advanced mechanics course that's helpful in anything from qm to gr, including at research level. a first random topic that comes to mind is the physics of constrained systems.

 

[G01]

Also remember that a PhD in physics will be expected to have a broad knowledge of all areas of physics, along with their chosen field of specialization.

For instance, people will expect me to know something about quantum mechanics (beyond what the average undergraduate knows) even though my research is in metamaterials and and ultra-fast optics.

 

[Aimless]

At my school, graduate Classical Mechanics also doubles as a graduate level math methods course. I suspect my school is not the only one for which this is true.

 

[planethunter]

Why do first-year grad students take classical mechanics, besides those wanting to analyze mechanical systems?

This would be a course along the lines of Goldstein, etc.

Do some of the concepts/methods show up later in quantum mechanics, nuclear physics?

If they skipped this mechanics course, would they not understand the material as well in these two latter topics of study?

I am starting classical mechanics on Monday using Landau (ima master’s student). It’s pretty standard in most of the universities that I have researched for classical mechanics to be taken in your first year of graduate school. It may not be the most exciting of physics subjects, but from what I understand, you really need it when you take QM and relativity or astrophysics

 

[twofish-quant]

Why do first-year grad students take classical mechanics, besides those wanting to analyze mechanical systems?

For many of the same reasons that first year undergraduates take classical mechanics. People have an intuition about how classical systems work, and once you connect that intuition with mathematical concepts, it makes it easier to go into the places where you don't have that intuition.

Do some of the concepts/methods show up later in quantum mechanics, nuclear physics?

Pretty much all of them do. Langrangians. Hamiltonians. Functional analysis.

If they skipped this mechanics course, would they not understand the material as well in these two latter topics of study?

Yes. You will find it a *LOT* harder to understand quantum field theory if you don't have a firm grasp of classical field theory.

 

[Lavabug]

At my university, we use Landau's & Goldstein's for two sophomore undergraduate level mechanics courses (one is an "all-in-one" course with Lagrangian mechanics, fluids, waves, & SR. The other is a pure analytical mechanics curriculum(rigid bodies, small oscillations, variational calc and H-J theory).

I'd say small oscillations and variational calculus are ubiquitous throughout all of physics.

 

[Angry Citizen]

Not to derail the thread, but if first year grad students take classical mechanics, why do people take classical mechanics as a junior? What is explored in grad school that is not explored in the undergrad class?

 

[G01]

Not to derail the thread, but if first year grad students take classical mechanics, why do people take classical mechanics as a junior? What is explored in grad school that is not explored in the undergrad class?

For the same reason that you had to take an introductory physics course before you take Junior level classical mechanics. Physics education builds upon previous knowledge. The best way to teach physics is not to throw students into the deep end with sharks, but to slowly get them wet and expose them to different swimming (and shark-killing, in this case) techniques.

In graduate school you are going to take more advanced courses in all the "pillars" of physics: Classical Mechanics, Quantum Mechanics, Electrodynamics, and Statistical Mechanics. In every case, you will cover the subject in much more depth than you would as an undergraduate. You will go into much greater mathematical detail, and also solve much harder problems.

As an example, I never covered Poisson brackets and non-holonomic systems as an undergrad. I also only had a cursory introduction to classical field theory as an undergrad.

 

[Lavabug]

As an example, I never covered Poisson brackets and non-holonomic systems as an undergrad.

Out of curiosity, how many classical mechanics courses did you have as an undergrad apart from 1st year general physics courses?

 

[G01]

Out of curiosity, how many classical mechanics courses did you have as an undergrad apart from 1st year general physics courses?

Besides general course, I had one semester long Junior year classical mechanics course. It covered Newtonian mechanics, Lagrangian and Hamiltonian mechanics, two body central force problems, coupled oscillators, special relativity, and we briefly touched on classical scattering problems. We didn't really get to continuous systems and classical field theory and the like. A full year long course may have some time to hit on the topics I mentioned in my above post, but I'm not sure.

 

[nlsherrill]

There are a lot of things in modern physics that have foundations from classical mechanics, like twofish said, lagrangian/hamiltonian formalism being the most obvious(to me).

Reading this thread is interesting though. I was surprised to hear from Lavabug that you use Goldstein/Landau for undergraduate mechanics. These texts are used in the graduate mechanics courses at my school, and we use Classical Dynamics of Particles and Systems by Thornton/Marion. I've skimmed through Goldstein's text and I have to say it is *quite* mathematical and more "mature" than Thornton/Marion.

Angry Citizen-

I think at the graduate level(with maybe the exception of Lavabugs school) you explore more deeply into Hamiltonian dynamics and more precisely, Hamilton-Jacobi theory... Also, at the undergraduate level(in my experience) when dealing with lagrangians, we usually stick with conservative systems(i.e. no friction/damping). I think they introduce the dissipation function in Goldstein.

Also, it seems highly dependent on how much the professor wants to cover. For example, in CM 1 we focused quite a bit on nonlinear oscillations, which is usually regarded as a special topic. The class from the previous year did not cover this in detail, but instead covered things like Poisson Brackets, which we did not. Also, the previous year frequently used the levi-civita density in coordinate transformations(which has the role as a rank 3 tensor apparently) and we did not cover it at all. Unfortunately for me in CM 2 now, we have the professor from the previous year so I now have to learn his emphasis now.

 

[Lavabug]

Reading this thread is interesting though. I was surprised to hear from Lavabug that you use Goldstein/Landau for undergraduate mechanics. These texts are used in the graduate mechanics courses at my school, and we use Classical Dynamics of Particles and Systems by Thornton/Marion. I've skimmed through Goldstein's text and I have to say it is *quite* mathematical and more "mature" than Thornton/Marion.

Much to my class' annoyance. :) From what I've gathered so far, it looks like the higher level E&M and mechanics courses are reserved for grad school in the US. Here in Spain and some other parts of the world, they're mandatory undergrad courses, whereas grad school is reserved purely for specialty courses in whatever masters degree one chooses. The undergrad degree also lasted 5 years formerly, now its 4 but beyond my first year, I still have to take a full year's worth in mechanics, EM, QM(Cohen), thermo/statistical and Optics(geometric and electromagnetic). Other mandatory courses include: solid-state(3rd year), nuclear/particle(4th), general relativity(4th) & circuit theory (4th).

Classical electrodynamics (Jackson) was also a mandatory 3rd year course in the now-extinct 5-year program, as well as a math course (elective) in tensors, integral equations, and group theory. Shame cause I really would have liked to take both and QFT(formerly 4-5th year elective, now only available in a masters program).

 

[Angry Citizen]

So hmm, would an aerospace engineering grad student benefit from this level of classical mechanics? Just thinking ahead here, I'm actually still very much an undergrad.

 

[nlsherrill]

So hmm, would an aerospace engineering grad student benefit from this level of classical mechanics? Just thinking ahead here, I'm actually still very much an undergrad.

Hmmm I am honestly not sure on how applicable these courses would be to an AE graduate. I would assume it couldn't hurt, but I do not really know what someone in that field has to know. I *think* engineers focus more on vectorial mechanics versus a physicist who after their introductory courses tend to shift emphasis to variational mechanics/methods.

Looking over the material we are supposed to be covering in CM 2, it seems like a fair amount of these topics would have applications to one interested in space flight. We are going to cover topics like central force motion/orbital dynamics, rigid body dynamics, and dynamics of systems of particles. I imagine an astronautical engineer would need to have a firm grasp on topics like these for satellite/space ship motion. But hey, this is just a guess. I would ask your adviser what physics is necessary to know in the AE field or show them the course description of classical mechanics at your school and see what they say.

Just one more thing. Even if its not entirely applicable, the course itself is incredibly interesting. A lot of people don't find intro mechanics that interesting, but classical mechanics goes so much further into detail. Its a very different course than the intro version. If you are interested in the topic it may just be plain fun to learn. Just a warning though, its pretty time consuming.

 

[Lavabug]

Do you use vector mechanics/Newtonian formalism when studying orbital motion at that level? Cause that seems like the main reason one would want to use Lagrangian or Hamiltonian mechanics to solve for motion, wasn't that the main driving force behind their development?