Setting up a function to use with ODE solver

Hi. I'm working on a project using one of the ode solvers in matlab to generate a numerical solution to an ode for charged particle motion. I've used the ODE solver before but I'm just confused on how to set up my function for my equation. The equation I'm using to solve for general motion for the charged particle is:

m*(dv/dt) = q(v x B)

I know that the general analytic solution to this problem is r = mV/qB but I am unsure of how to work this out with the ODE solution. If anyone could give me some help setting up my function it would be greatly appreciated. Thank you.

[Azzi Abdelmalek]

What are variables and constants and what is r?

[Sean]

m = mass q = charge of particle v = perpendicular velocity B = magnetic field strength r = radius of motion of the particle

[Azzi Abdelmalek]

This is your equation

m*(dv/dt) = q(v x B)

There is no r in it, and what is x? which variable are you looking for?

[Sean]

x is just supposed to be the cross product, r is what the equation can be simplified to if instead of using dv/dt we use a for acceleration and then substitute in rotational acceleration = v^2/r and then solving for that radius. I'm trying to solve for dv/dt so that I can plot out the orbit of the particle

[Sean]

This is what I have so far, I split up the velocity into x and y components:

    function drdt = diffrv(t, rv)
q = 1.60217646 * 10^-19; % coulombs charge of electron
m = 9.10938188 * 10^-31; % mass of electron 
B = 10^-9;
drdt = zeros(4,1);
drdt(1) = (q/m)*rv(2)*B;
drdt(2) = -(q/m)*rv(1)*B;
drdt(3) = (q/m)*drdt(2)*B;
drdt(4) = -(q/m)*drdt(1)*B;
drdt = [drdt(1);drdt(2);drdt(3);drdt(4)]

end

And for the actual solving:

    init(1) = 5000; % x component velocity
init(2) = 3000; % y component velocity
init(3) = 0;
init(4) = 0;
tspan = 0:1:100;
options = odeset('RelTol', 1e-11, 'AbsTol', 1e-11);
[t,rdot] = ode45('diffrv',tspan,init,options)
plot(rdot(:,3),rdot(:,4))
  end

[Sean]

This seems to work correctly also but it takes an insanely long amount of time to run

Answer 1

[Babak]

You need to write the equation in the dimentionless form. You cannot just simply write numbers like

 m = 9.10938188 * 10^-31

in MATLAB and excpect it work fine!

Answer 2

[Jan]

How much faster is this:

function drdt = diffrv(t, rv)
q = 1.60217646e-19; % Avoid expensive power operation
m = 9.10938188e-31; % mass of electron 
B = 1e-9;
c = (q/m)*B;
drdt = zeros(4,1);
drdt(1) = c*rv(2);
drdt(2) = -c*rv(1);
drdt(3) = c*drdt(2);
drdt(4) = -c*drdt(1);
% Useless: drdt = [drdt(1);drdt(2);drdt(3);drdt(4)]
end

When the relative and absolute tolerances are such tiny, long computing times can be expected. Unfortunately the results are not necessarily better, because small tolerances lead to a high number of integration steps and the rounding errors accumulate.