MATLAB: Differentiation for timing input

Question

I want to differentiate these equation with matlab.I use input v1 as constant 1 and for input v2 use signal builder for ( time 1 to 4 input 0;time 4 to 6 input 1,time 6 to 10 input 0).please help me.

x1dot=v1*sin(x3);

x2dot=v1*cos(x3);

x3dot=v2;

Answer 1

This is a system of ODE. You can use ode45() to find a solution

tspan = [0 10];
IC = [0; 0; 0]; % initial condition
[t, X] = ode45(@odeFun, tspan, IC);
plot(t, X);
legend({'x1', 'x2', 'x3'}, 'FontSize', 16);
function xdot = odeFun(t, x)
    v1 = 1;
    
    if t < 4
        v2 = 0;
    elseif t < 6
        v2 = 1;
    else
        v2 = 0;
    end
    
    x3 = x(3);
    
    x1dot=v1*sin(x3);
    x2dot=v1*cos(x3);
    x3dot=v2;
    
    xdot = [x1dot; x2dot; x3dot];
end