Recent content by adartsesirhc

Hmm... I clicked on the link, but it appears to be invalid.

Homework Statement Zwiebach's A First Course in String Theory Quick Calculation 2.5: Consider the plane (x,y) with the identification (x,y)\rightarrow (x+2\pi R,y+2\pi R). What is the resulting space? Homework Equations A one dimensional line with identification x\rightarrow x+2\pi...

Sorry, I meant \int \frac{4cos(t)}{(2+sin(t))^2}dt

Homework Statement Use substitution to evaluate the integral. \int \frac{4cos(t)}{(2+sin(t))^2}dt Homework Equations None, really.The Attempt at a Solution I'm not sure what to use as u, for the substitution. I've tried (2+sin(t))^2, as well as other attempts, but I can't seem to find anything.

Hi, I'm a high school senior that's just been admitted to Caltech. They sent me their course catalog in the mail, and I've been looking over it this week. I want to major in physics, and someday study elementary particles, gravitation, and string theory. What math should I take? Caltech...

I've taken a course in Linear Algebra, so I'm used to working with vector spaces. But now, I'm reading Griffith's Introduction to Elementary Particles, and it talks about groups having closure, an identity, an inverse, and being associative. With the exception of commutativity (unless the...

Well, as far as I can see in derivations, a rheonomic constraint shouldn't really matter. But what should I do with the time? Should I just ignore it and use the Euler-Lagrange equation normally, or should I treat it as a generalized coordinate? And does anyone have any suggestions for the...

How does a Lagrangian change for a system with a rheonomic constraint? As far as I can see in the derivations, it shouldn't seem to matter, but I just want to make sure. And if I have a rheonomic constraint, what should I do with the time? Should I just ignore it and use the Euler-Lagrange...

I saw this video on YouTube, and I just understood what it means by "inverted pendulum": I guess the one in the problem is identical to this one, exact that the motion is vertical and given by the equation above. So any ideas on the kinetic and potential energies, or on how the...

Nope. If v=2^{5x}ln5, then dv=2^{5x}(ln5)^{2}dx. Then v has to be a function so that if you take the derivative, that ln5 cancels out.

Also, when the problem says 'inverted pendulum', does this mean that there's some kind of force preventing the pendulum from rotating to an equilibrium position (i.e. hanging straight down)? When I think of it, I visualize something like a metronome... does this sound right?

An inverted pendulum consists of a particle of mass m supported by a rigid massless rod of length l. The pivot O has a vertical motion given by z=Asin\omega t. Obtain the Lagrangian and find the differential equation of motion. I'm not sure how to obtain the kinetic and potential...

Yeah, I know it's definitely not new - it's probably been done since Lagrange's time - but one of my teachers recommended showing it to the admissions office. I have noticed a couple of mistakes, though. First, the U in the last line shouldn't be a vector - potential energy is a scalar...

Hi, all. A friend challenged me to prove that F = -grad(U), and now that I did, I'm thinking of submitting it to the university I'm applying to. Before I do so, I want to see if this is right. Theorem: For a particle in a conservative force field, F = -grad(U). Proof: In a conservative...

Basically, to find an antiderivative, you have to think up a function that, if you take its derivative, you would get your original function back again. Now, the Power Rule of derivative says that if f(x) = ax^n, then f'(x) = anx^{n-1}. So use this backwards: You have f(x) = x^2. Your...