Not sure why you bumped a year old thread, but can't you just solve this by reducing it to a system of first order ODES and applying a runge kutta method or something similar?
In sphereical coordinates you know that x=\rho\cos\theta\sin\phi, y=\rho\sin\theta\sin\phi and z=\rho\cos\phi
You can use this to find limits for \rho.
If you draw the x-z or y-z plane intercept this can help you find \phi
If the reaction isn't 0 order, then it will generally decrease as time goes on if the conditions are held constant. You're correct, it's because there's less reactants. By collision theory, the reactants must collide with the correct alignment and with E > E_a. As you decrease the number of...
Are you asking how to store the variables so that it doesn't get overwritten each time? If so, you could probably do that using cell arrays/structures/arrays
For example:
rndx = 1;
for r=1:5;
tetandx = 1;
for teta=10:10:360;
sigmar= ...
data(1,tetandx,rndx) = sigmar;
tetandx =...