Hi, I'm working on a function that will calculate the time it takes for an object to go down a "curve line" more specifically a cycloid and I got these equations to determine the amount of time it takes to reach the bottom of the halfpipe:
p(t) = c(φ(t))
if V(t):=[φ(t), φ'(t)]
then, dV/dt = F(V):= [V2, ((-sin(V1)(RV2^2-g))/(2*R(1-cos(V1))))]
and the initial conditions are
V(0) = [φ(t), 0]
R=1 G=9.8m/s
How I can translate this set of equations into a function to be able to implement ode45 or use Runge Kuta method? I know that I should write the functions and later on their derivatives for the Runge Kuta, and the function itself with another function for ode45.
I have this but I do not feel confident with the code. How can I improve it or make it work?
y(1) = [phi,0];
F_xy = @(V1,V2) (V2,(-sin(V1)*(R*V2^2-g))/(2*R(1-cos(V1)))))
for i=1:(length(x)-1)
k_1 = F_xy(x(i),y(i));
k_2 = F_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);
k_3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_2));
k_4 = F_xy((x(i)+h),(y(i)+k_3*h));
y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h;
