How to write an event function to stop at second or third x axis crossing.

I need my function to stop at a specific x crossing, but it has several and the one I need is the third that occurs over time. I tried writing a loop that made the stopping of the function contingent on multiple values (y component = 0 and y velocity being positive). But it's not stopping the function at all.

function [value, isterminal, direction] = xcross(t, state_xyz, mu)

v1 = state_xyz(2);

v2 = state_xyz(5);

value = v1;

if v1 == 0 && v2 > 0

isterminal = 1;

else

isterminal = 0;

end

direction = 0;

end

Answer 1

[Sameer]

Hi @Madeleine

To stop at the third x-axis crossing, you need to count the number of crossings and stop when the count reaches three. You can achieve this by using a "persistent" variable to keep track of the number of crossings that have occurred.

https://www.mathworks.com/help/releases/R2023b/matlab/ref/persistent.html

Here's how you can modify your function:

function [value, isterminal, direction] = xcross(t, state_xyz, mu)
    persistent crossing_count;
    
    if isempty(crossing_count)
        crossing_count = 0; 
    end
    
    v1 = state_xyz(2); 
    v2 = state_xyz(5); 
    
    value = v1;
    direction = 0; 
    
    % Check if it's a crossing
    if v1 == 0 && v2 > 0
        crossing_count = crossing_count + 1;
    end
    
    % Stop at the third crossing
    if crossing_count == 3
        isterminal = 1;
    else
        isterminal = 0;
    end
end

Hope this helps!

Answer 2

[Torsten]

I'd make the solver stop at each x-crossing. After it returns control to the calling program, add 1 to the number of crossings and restart the solver if the third crossing has not yet been reached or stop the integration if the number of crossings has reached three.

Take a look at the ballode example on how to save the solution so far and restart the solver in a loop:

https://uk.mathworks.com/help/matlab/math/ode-event-location.html

If you manage to modify the example such that the solver stops at the third time the ball hit the ground, you can easily use the code in your application.