Changing the differential equation using even functions (with ODE23)

am using event functions for when the mass is decoupled from the 2nd spring (see diagram below), however despite changing the value of s2_on within the function, it does not appear that the ode is changing when the event is reached. (The event is definitely triggering as I found from making it terminal).

function HarmonicMotion   
%% Calculation and Plotting
    function plot_nf(data) % Plots values for no fluids using ODE 45
        % Event Functions
            inc = 0;
            function [position, isterminal, direction] = isGapDec(t, x)
                d = data(5);
                position = x(1) - d;
                isterminal = 0;  % Doesn't end the ode
                direction = -1;  % For when mass decoupled
                s2_on = 0; % i.e Cancels effect of s2_on in ode
            end
            function [val, isterminal, direction] = isGapInc(t, x)
                d = data(5);
                val = x(1) - d;
                isterminal = 0;  % Doesn't end the ode
                direction = 1;   % When mass 'attatched'
                s2_on = 1;
            end
            disp(inc)
            opt1 = odeset('Stats', 'on', 'Events', @isGapInc);
            opt2 = odeset(opt1, 'Events', @isGapDec);
            
        function [disp_vel] = calc_nf(xv, data)
            % Extract data
            m_c = data(1); s1 = data(2); s2 = data(3); c = data(4); 
            d = data(5); t_total = data(6); dt = data(7); xv0(1) = data(8);
            m_f_max = data(9); fluid_r = data(10);
            s2_on = 1;
            x = xv(1); v = xv(2); %Sets x = xv(1), and v = xv(2) i.e d(x)/dt
            
            disp_vel = [v; -(s1*x + c*v + s2*s2_on*(x-d))/m_c]; %%%% THE DIFFERENTIAL EQ. %%%, WITH S2_ON THE ISSUE
        end
        [t, xv1] = ode23(@(t,x) calc_nf(x, data), [0:dt:t_total], xv0, opt2); % passes xv1 through calc_nf with boundary cond xv0
        accel = diff(xv1(:,2))./diff(t);
        accel(end+1) = 0;
        
        figure('Name','Without Fluid','NumberTitle','off');
        hold on
        plot(t, [xv1(:,1), xv1(:,2), accel], [0 t_total], [d d], 'k-.');
        title('Plot of Harmonic Motion without Fluid');
        grid minor; 
        xlabel('time / s');legend('Displacement / m', 'Velocity / ms^{-1}', 'Acceleration / ms^{-2}', 'Gap'); % Labels graph
        hold off;
    end

   

%% Default values and Table
%%% Default Values Array %%%
    m_c = 2;        % Container Mass
    s1 = 16;        % Spring Constant 1
    s2 = 20;        % Spring Constant 2
    c = 2;          % Damping Coef
    d = 0.6;        % Gap
    t_total = 2;    % Total Integration Time
    dt = 0.01;      % Integration step
    xv0 = [2 0];    % Init Displacement & velocity
    m_f_max = 4;    % Max mass of fluid
    fluid_r = 1;    % Fluid mass rate
    default_vals = [2 16 20 10 0.6 2 0.01 2 4 1]; % For use in table
    data = [m_c s1 s2 c d t_total dt xv0(1) m_f_max fluid_r]; % For use in functions, and table
    
    plot_nf(data);
end

I

Answer 1

[Arnav]

Hi Fawaz,

Attempting to change the value of s2_on inside the event functions will not affect the ODE solver, because s2_on is scoped locally within those event functions. You can create a persistent variable inside the HarmonicMotion function as follows:

function HarmonicMotion   
    persistent s_on % persistent variable

    function plot_nf(data) % Plots values for no fluids using ODE 45
        % rest of the code

    end

    % rest of the code
end

This will create a persistent variable that is shared between the event functions. You may refer to the following MATLAB documentation link for more information about how variables are scoped:

https://www.mathworks.com/help/matlab/matlab_prog/base-and-function-workspaces.html

Hope it helps!