Recent content by maves

Homework Statement I am analysing intensities of some pictures. There are specific regions of higher intensities and so far i have managed to locate those regions automatically in Mathematica and the program returns the average intensity and standard deviation on this regions ("circles"), so I...

I tried to approximate the integrands with a series and integrate them after that ... and it turned out, that Mathematica 8 integrates in a different way than the earlier versions of the program (I tested this on an expression I evaluated some time ago when I had M.6 or 7 and it put out a...

Thank you very much for your help, I will consider this idea. And about the energies ... not that they are not constant, they actually fluctuate around one value, but the amplitude is mostly quite big ... could this be only due to numerical errors? :S I also figured out, that if I enlarge...

Potential in xy plane are concentric circles, potential in xz plane looks like this ... (the second picture is zoomed and shows, where the torus is located)

Yes, I have found an orbit like that, but the professor also advised me to look for the orbits, that go around the torus like a ring (xz plane) - to compare their energies. But my trajectories always go around the whole torus. Edit: I attached a file of an example, that seems pretty illogical...

Hello again, maybe another stupid question, but still - what exactly should I consider as orbits? For instance, I found some nice rosettes in xy plane (see in attachment), but when I calculate their energy (E=T+U), they don't seem to be constant in every point. Furthermore, I am positive...

Aaaargh... of course! :) Thanks.

^Thank you for your answer, I will try doing it that way, and ask again, if another problem occurs. And by the way, a little problem with the sign, that bothers me, and I don't understand, where I have missed it: If the potential is U\,(r,z) = -G\rho...

I see. I don't think that the geometry here is so important, as I get similar results for square cross-section. I will append a few pictures for better understanding of the geometry. The first picture shows you, how the coordinate system is set. The point inside a torus has coordinates...

Homework Statement We have a homogenous toroidal planet. Its cross-section is half of a square, so that the hypotenuse is parallel to the z-axis. Find the orbits of constant (especially lowest) energy around that planet. Homework Equations 1) Homogenous planet: \rho=const. 2) Potential...

I would move the picture to the directory, where your latex document is, or at least to its subfolder - in this case you don't even need to write the full path to the picture, only {picture.jpg} or {subfolder/picture.jpg}. It works for sure :)

So I still have hope, that maybe someone could help me :) What I figured out until now is, that i forgot to take into account one minus sign, which made everything wrong, as the gravitational force in my calculations was repulsive and so the trajectory was hyperbolic (looked like linear on first...

Yes, LCKurtz, you understood me correctly, thank you. So I was wondering, if maybe anyone else could help me out here: The expression for the eigenmodes of the square drum, that I got, taking homogenous boundary conditions of 3rd kind, into account, is: where k_{xm}, k_{yn}, \alpha are...

Hello, this is me again, I unfortunately still haven't managed to finish my work yet. LCKurtz, I think you were right, it is beter to use the combination of sines and cosines in my solution, so now I have: X=C\cos{k_x x}+D\sin{k_x x} \\ Y= E\cos{k_y y}+F\sin{k_y y} I figured out, that the...

LCKUrtz, first of all I would like to thank you for your answer. Only now I can see I didn't make some of my assumptions clear, so you couldn't really understand my question. What I wanted to say is that I followed all of the steps that the original poster (jamesmcm) did in his first post of...