Tips for mastering classical mechanics?

>>8348946
Whatever the angular inertia of the flywheel your considering, its not enough.

>>8348960
I'll keep that in mind

>>8348976
>That's a nice Lagrangian you got there
>You even have the right amount of coordinates!
>Oh wait, I see you forgot to couple your equations of motion

Every goddamn time.

>>8348984
good to remember

>>8348989
What level classical mechanics are you taking, though? In all seriousness. First semester intro, upper level undergraduate, or graduate?

>>8348994
I'm not taking the class, but I need to get good so that I can confidently apply to a mechanical engineering masters program, even though my undergraduate is math.

>>8349007
Oh, you'd probably enjoy classical mechanics then. It's probably one of the purest applications of mathematics to real world phenomena. As long as your vector calculus and differential equations are strong you should have a pretty good time of it. You'll just need to watch out for vocab terms, especially when you reach Lagrangian mechanics if you're looking to go that deep.

>>8349018
> vector calculus and differential equations
vector is no problem, differential is just a bit rusty. I'm definitely seeking a deep understanding of Lagrangian mechanics, do you mind telling me any of your other reflections on learning that subject?

>>8349026
You'll need every trick in the differential equations toolbook I'm afraid. Lagrangian mechanics IS the process of solving a second order differential equation to find explicit equations of motion (though, truth be told, analytical solutions are only available for the nicest of systems, the rest have to be solved computationally). The other side of it is, of course, Hamiltonian mechanics, which is basically a deeper formulation of Lagrangian mechanics (we just started the derivation in my graduate mechanics class and it's mind bending). It's a delicate subject with lots of ins and outs, especially once you hit Lagrangian mech. You should start with simple Newtonian mechanics, this is simple F=ma stuff, and you'll find it's a nice straightforward way to deduce information about physical systems. From there you'll find out that there are some systems where Newtonian mechanics simply isn't enough or is too convoluted, and this is where Lagrangian mechanics will come into play, as well as Hamiltonian mechanics. And both of these will rely on the careful interplay of derivatives and products of derivatives and sums of products of derivatives. The higher you go the more quickly things get difficult past the broad overview, so a concrete foundation is a must. Plenty of resources are available, such as MIT's opencourseware (which I haven't checked, but there's probably a classical mech course on there), and a dozen or so books floating around the internet. "Classical Mechanics" by John Taylor is a pretty good place to start, and if that's too soft, try the same title by a dude named Goldstein, which is usually assigned for graduate level classes.

>>8349046
I know I mentioned that you need every tool in differential equations, but just to drive that home, Newton's second law, F=ma, is already a differential equation, just for example.

>>8349046
great tips, very encouraging.
Can I ask about your focus? Do you use mechanics in your work/research?

>>8349050
yeah It's OK, I didn't have any problems it's just been a couple years.

>>8349051
I'm actually in graduate school for nuclear physics haha. I'm god awful at classical mechanics; was in undergraduate, am in graduate. It's just a ringer you have to go through. My primary research is data acquisition and analysis at the Relativistic Heavy Ion Collider at Brookhaven National Labs. I guess I couldn't truthfully answer no to your question though. Particle collisions follow a lot of the same rules as classical collisions. If two things hit each other, they'll fly off a certain way with a certain amount of energy and momentum, etc. So while I don't spend my time solving Lagrangians for particle beam interactions, the research I do wouldn't exist without classical mechanics and its underlying principles.

>>8349066
Brookhaven?? don't josh me. Right in my area. You at Stony Brook?

>>8349075
Nope, my advisor went there though! I'm down in Atlanta, part of a collaboration group working on the new detector that's being installed (well, really it's an upgrade to the one that's already there).

>>8349081
Sounds enthralling. Did you come up here or are you doing remote analysis?

Either way, it's funny that you're working with Brookhaven. I grew up and still reside in the area and I did my undergrad in NYC.

>>8349083
Remote analysis at the moment. Well, I still need to turn in some forms (I'm fucking swamped at the moment and can barely find time to do little things like email pdfs), but I will probably be up there over the summer if all goes well. But yes, quite the small world, isn't it?

>>8349091
It is.