Modeling forces in a sphere using a system of ODEs

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Steph Walker
Steph Walker 2012-5-19
Hello,
I'd like to use matlab to model force interactions between 2 electrons in a helium atom. I'm familiar with ode45 but am having a little trouble because my spherical coordinates r,theta,phi need to be redefined every iteration.
I have a starting velocity and position r,theta,phi for each particle and equations of the forces between the nucleus and each electron which should guide the movement. But, I am not sure how to introduce a position vector into an ode and have it change each time step to represent the result of the forces.
Here would be my input:
pos1=[r,theta,phi] % Starting values
velocity= some value
Particle 1 eq:
prt1eq=-k*2*e^2/me*(pos1)^2+k*e^2/me*(pos1-pos2)^2;
Particle 2 eq:
prt2eq=-k*2*e^2/me*(pos2)^2+k*e^2/me*(pos2-pos1)^2;
The equations are coupled. I'd like to do many iterations to map out the force values and corresponding positions.
Can someone point me in the right direction?
Thanks

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