to make it simple, vector A = (1,2,3) in the cartesian coordinates and it is the solid angle over a sphere. I'm pretty sure there's a way to simplify this. I've tried multiplying top and bottom by 1+A.Omega and then separating them into two integrals. One is an even function and one is an odd...
sorry, i did a variable change because i tried to save time by just using x and y instead of greek symbols mu and gamma.
i hope that clears it up that they are not cartesian coordinates.
i don't think the integral is in cartesian coordinates. x ranges from (-1,1) and y from (0,2pi). I'm not sure what this coordinate system is called, but it's different. so ur suggestion wouldn't work.
can someone please give me some help on this integral. it should be solvable analytically.
\int^{1}_{-1}\int^{2\pi}_{0}\frac{1}{2+x+\sqrt{1-x^2}cos(y)+\sqrt{1-x^2}sin(y)}dxdy
i have a related question. what happens when u pluck two guitar strings together, but one of the string is fretted. let's assume the fretted string is just one octave higher.
so for example, the 5th string is open and the 3rd string is fretted on the 2nd fret. u pluck these two strings...
Two group slab reactor
Would you say finding the fluxes for a two group is possible analytically? I have to solve the two equations below:
-D_{2}d^{2}\phi_{1}/dx^{2}+\Sigma_{R1}\phi_{1}=1/k(v_{1}\Sigma_{f1}\phi_{1}+v_{2}\Sigma_{f2}\phi_{2})...
I'm using matlab's [V,D]=eig(A,B) function to find the eigenvectors and eigenvalues given two full matrices of A and B.
I know the eigenvectors that I get are not orthonormalized, so how do I do this?
Let's say I'm solving a simple Sturm-Liouville problem like...
Homework Statement
50uA beam of 1MeV proton
Target = Iron of 0.05um thick
Calculate scattered current density at distance 5 cm at 20 degrees angle
Homework Equations
\sigma(E,\theta) = \pi*Z_{1}Z_{2}e^{4}(M_{1}/M_{2})/ET^{2}The Attempt at a Solution
I figured the probability of scattering to...
G'' = -kG
k is a constant
solving this ODE, r = +/- sqrt(-k)
if k > 0, then r = +/- sqrt(k)i
so G is in the form Acos(sqrt(k)x) + Bsin(sqrt(k)x)
so, what if k is a complex number, then
r = +/- sqrt(-ki)
then what is the form of G?
i'm not sure but that's what i was asked.
so if it's atomic lattice, then i would be right to say the corners are 1/8 and the middle is 1 atom? but isn't the middle atom shared by other diagnoal lattice?
i'd like to know what is the number of atoms per unit length for an atomic chain in the [1 1 1] direction of a BCC structure.
i can figure out the unit length, however I'm not sure how many atoms to use. Is it 1/8+1/8+1? That means 1/8s for the two corner atoms and 1 atom for the middle? or...