Plotting the solution to a system of second order differential equations

Question

Aleem Andrew 2020-4-3

0
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https://ww2.mathworks.cn/matlabcentral/answers/514984-plotting-the-solution-to-a-system-of-second-order-differential-equations

评论： Aleem Andrew 2020-4-3

I am having difficulty interpreting the plots generated by the following code. Is there a way I can generate a single plot instead of four plots, for example, the plot of θ(t) vs x(t)?

ode = @fun;
t = [0 10];
ic = [pi/3; 0; 0; 0]; % [θ θ' x x'] 
[t,x] = ode45(ode, t, ic);
plot(t,x);
xlabel('x(t)');
ylabel('θ(t)');
function dydx = fun(t,x)
    L = 0.5; g = 9.81;  
    dydx = zeros(4,1);
    dydx(1) = x(2);
    dydx(2) = (4*sin(x(1))*(5*L*cos(x(1))*x(2)^2 + 6*g))/(L*(20*cos(x(1))^2 - 23));
    dydx(3) = x(4);
    dydx(4) = -(5*sin(x(1))*(23*L*x(2)^2 + 24*g*cos(x(1))))/(6*(20*cos(x(1))^2 - 23));
end

The code generates four plots, only one of which satisfies the initial conditions (θ = pi/3 and x = 0) while I do not understand what the other plots represent.