L = 100
m = 1/100
alpha = 5/(10**5)
k = alpha/m


def f(X, t):
    x_deriv = k*(V_w(X, t)[0]-X[0])
    y_deriv = k*(V_w(X, t)[1]-X[1])
    return [x_deriv, y_deriv]

def V_w(X, t):
    x = X[0]
    y = X[1]
    R = np.sqrt(x*x+y*y)
    T = 24*3600  #sekunder
    x_vec = -(2*np.pi*R/T)*y/R
    y_vec = (2*np.pi*R/T)*x/R
    return [x_vec, y_vec]

def forward_Euler(f, h, X, t):
    x_koord = X[0] + h*f(X, t)[0]
    y_koord = X[1] + h*f(X, t)[1]
    return [x_koord, y_koord]

def explicit_trapezoid_eq1(f, h, X, V t):
    [u_temp, v_temp] = forward_Euler(f, h, V, t)
    u =
    x_koord = X[0] + (h/2)*(f(X, t)+f([x_temp,y_temp], t))
    y_koord = X[1] + (h/2)*(f_y(X, t) + f_y([x_temp, y_temp], t))
    return x_koord, y_koord