I've tried to model the circle shape in presence of gravitational waves, but the points lying on the x-axis don't move.
I computed the dependence of this component by hand, and it should change with time. It seems like something is wrong with the function Len_Linit, since I checked all others independently and everything was fine.
%matplotlib notebook
import matplotlib.pyplot as plt
import matplotlib.animation as animation
import numpy as np
omega = 1
L0 = 2
l = 1
def h_ij(omega, t):
h = np.zeros((3,3))
matrix_1 = np.array([[1,0,0],[0,-1,0],[0,0,0]])
matrix_2 = np.array([[0,1,0],[1,0,0],[0,0,0]])
h += -np.cos(2*omega*t)*matrix_1 - np.sin(2*omega*t)*matrix_2
return h
def n_vec(N):
n = np.zeros((N, 3))
for i in range(N):
n[i, 0] += np.cos((2*np.pi*i)/N)
n[i, 1] += np.sin((2*np.pi*i)/N)
return n
def Len_Linit(N, omega, t, l, L0):
Len_arr = np.zeros(N)
for i in range(N):
Len_arr[i] += L0
h = h_ij(omega, t)
n = n_vec(N)
for i in range(N):
for k in range(3):
for l in range(3):
Len_arr[i] += (l/2)*h[k,l]*n[i,k]*n[i,l]
return Len_arr
def get_coords_of_Li(N, omega, t, l, L0):
coords = np.zeros((N+1, 3))
Li_0 = Len_Linit(N, omega, t, l, L0)
n = n_vec(N)
for i in range(N):
coords[i,0]+= Li_0[i]*n[i, 0]
coords[i,1]+= Li_0[i]*n[i, 1]
coords[N, 0]+= coords[0, 0]
coords[N, 1]+= coords[0, 1]
return coords
fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(5, 5))
line, = plt.plot([], [], '-bo', lw=2) # the ball
axes.set_xlim(-3, 3)
axes.set_ylim(-3, 3)
plt.style.use("ggplot")
N = 14
def make_frame(i):
t = 0.1*i
coords = get_coords_of_Li(N, omega, t, l, L0)
thisx = coords[:, 0]
thisy = coords[:, 1]
line.set_data(thisx, thisy)
return line,
animation.FuncAnimation(fig, make_frame, interval=90)
