def SpiralGalaxy(num):
alpha = -2*4
r0 = 2e6
eps = 1e-3
randarr1 = np.random.rand(num)
randarr2 = np.random.rand(num)
K = 0.3*r0
#f_r = lambda r: 1/r0*np.exp(-r/r0)
#f_phi = lambda r: (np.sin(phi))**2
F_r = lambda r: 1-np.exp(-(r-K)/r0)
F_r = np.vectorize(F_r)
F_phi = lambda phi: 1/np.pi*(0.5*phi-0.25*np.sin(2*phi))
F_phi = np.vectorize(F_phi)
Finv_r = lambda p: -r0*np.log(1-p)+K
Finv_r = np.vectorize(Finv_r)
Finv_phi = lambda p: opt.newton((lambda x: F_phi(x)-p), p,tol = eps)
Finv_phi = np.vectorize(Finv_phi)
# p = np.arange(0.01,1,0.01)
# plt.plot(Finv_phi(p),p)
# x = np.arange(0,2*np.pi,0.1)
# plt.plot(x, F_phi(x))
# plt.show()
rarr = Finv_r(randarr1)
phiarr = Finv_phi(randarr2)
pos = np.array([[rarr[i]*np.cos(phiarr[i]+alpha*np.log(rarr[i])),rarr[i]*np.sin(phiarr[i]+alpha*np.log(rarr[i])),0] for i in range(len(randarr1))])
v = lambda r: np.sqrt(G*m*num*F_r(r)/r)
vel = np.array([[v(rarr[i])*(-np.sin(phiarr[i]+alpha*np.log(rarr[i]))),v(rarr[i])*(np.cos(phiarr[i]+alpha*np.log(rarr[i]))),0] for i in range(len(randarr1))])
col = np.array([[0.75-0.25*np.sin(phiarr[i]),0.75-0.25*np.sin(phiarr[i]+2*np.pi/3),0.75-0.25*np.sin(phiarr[i]-2*np.pi/3)] for i in range(len(randarr1))])
radius = RADIUS*np.ones((num,1))
mass = m*np.ones((pos.shape[0], 1))
return Bodies(pos, vel, mass = mass, radius=radius, dt=DT, color = col)
def motionless(num):
randarr = np.random.rand(num, 2)
pos = np.array([(STARTSIZE * rand[0] * np.cos(2 * np.pi * rand[1]),
STARTSIZE * rand[0] * np.sin(2 * np.pi * rand[1]), 0)
for rand in randarr])
VEL = 0
vel = np.array([(-VEL * np.sin(2 * np.pi * rand[1]),
VEL * np.cos(2 * np.pi * rand[1]), 0)
for rand in randarr])
return Bodies(pos, vel, radius=RADIUS, dt=DT)
def randombodiesUnif(num):
randarr = np.random.rand(num, 2)
pos = np.array([(STARTSIZE * rand[0] * np.cos(2 * np.pi * rand[1]),
STARTSIZE * rand[0] * np.sin(2 * np.pi * rand[1]), 0)
for rand in randarr])
VEL = np.sqrt(G * MASS * N / STARTSIZE)
vel = np.array([(-VEL * np.sin(2 * np.pi * rand[1]),
VEL * np.cos(2 * np.pi * rand[1]), 0)
for rand in randarr])
return Bodies(pos, vel, radius=RADIUS, dt=DT)
def RBDonutBlackHole(num):
randarr = np.random.rand(num,2)
pos = np.array([[(A + (B-A)*rand[0])*np.cos(2*np.pi*rand[1]),(A + (B-A)*rand[0])*np.sin(2*np.pi*rand[1]) ,np.random.normal(0,WITH) ] for rand in randarr])
v = lambda r: np.sqrt(G*M/r+G*m*num*(r-A)/((B-A)*r))
vel = np.array([[v(A+(B-A)*rand[0])*(-np.sin(2*np.pi*rand[1])),v(A+(B-A)*rand[0])*(np.cos(2*np.pi*rand[1])),0] for rand in randarr])
col = np.array([[0.75-0.25*np.sin(2*np.pi*rand[1]),0.75-0.25*np.sin(2*np.pi*rand[1]+2*np.pi/3),0.75-0.25*np.sin(2*np.pi*rand[1]-2*np.pi/3)] for rand in randarr])
radius = RADIUS*np.ones((num,1))
pos2 = np.concatenate((np.array([[0,0,0]]), pos), axis=0)
vel2 = np.concatenate((np.array([[0,0,0]]), vel), axis=0)
mass2 = np.concatenate((M*np.ones((1,1)),m*np.ones((pos.shape[0], 1))), axis=0)
col2 = np.concatenate((np.array([[0.2,0.2,0.2]]), col), axis=0)
radius2 = np.concatenate((np.array([[5*RADIUS]]),radius), axis = 0)
return Bodies(pos2, vel2, mass = mass2, radius=radius2, dt=DT, color = col2)
def randomBodiesBlackHole(num):
vel=np.zeros((num,3))
pos = (np.random.rand(num, 3))
for i in range(0,num):
pos[i][-1]=0
(pos[i][0],pos[i][1])=(pos[i][0]*STARTSIZE*np.cos(2*np.pi*pos[i][1]),pos[i][0]*STARTSIZE*np.sin(2*np.pi*pos[i][1]))
vel[i][0]=pos[i][1]*np.sqrt(G*m*N/STARTSIZE)/np.sqrt((pos[i][0])**2+(pos[i][1])**2)
vel[i][1]=-pos[i][0]*np.sqrt(G*m*N/STARTSIZE)/np.sqrt((pos[i][0])**2+(pos[i][1])**2)
print(pos.shape)
print(np.array([[0,0,0]]).shape)
pos2 = np.concatenate((np.array([[0,0,0]]), pos), axis=0)
vel2 = np.concatenate((np.array([[0,0,0]]), vel), axis=0)
mass2 = np.concatenate((M*np.ones((1,1)),m*np.ones((pos.shape[0], 1))), axis=0)
return Bodies(pos2, vel2, mass = mass2, radius=RADIUS, dt=DT)
def RBDonut(num):
randarr = np.random.rand(num, 2)
pos = np.array([[(A + (B - A) * rand[0]) * np.cos(2 * np.pi * rand[1]),
(A + (B - A) * rand[0]) * np.sin(2 * np.pi * rand[1]),
np.random.normal(0, WITH)] for rand in randarr])
v = lambda r: np.sqrt(G * m * num * (r - A) / ((B - A) * r))
vel = np.array([[
v(A + (B - A) * rand[0]) * (-np.sin(2 * np.pi * rand[1])),
v(A + (B - A) * rand[0]) * (np.cos(2 * np.pi * rand[1])), 0
] for rand in randarr])
col = np.array([[
0.75 - 0.25 * np.sin(2 * np.pi * rand[1]),
0.75 - 0.25 * np.sin(2 * np.pi * rand[1] + 2 * np.pi / 3),
0.75 - 0.25 * np.sin(2 * np.pi * rand[1] - 2 * np.pi / 3)
] for rand in randarr])
radius = RADIUS * np.ones((num, 1))
mass = m * np.ones((pos.shape[0], 1))
return Bodies(pos, vel, mass=mass, radius=radius, dt=DT, color=col)
def SpiralGalaxyBlackHole3D(num):
alpha = -2*2
r0 = 5e7
eps = 1e-3
M = 15 * num * m
randarr1 = np.random.rand(num)
randarr2 = np.random.rand(num)
K = 0.25*r0
#f_r = lambda r: 1/r0*np.exp(-r/r0)
#f_phi = lambda r: (np.sin(phi))**2
F_r = lambda r: 1-np.exp(-(r-K)/r0)
F_r = np.vectorize(F_r)
F_phi = lambda phi: 1/np.pi*(0.5*phi-0.25*np.sin(2*phi))
F_phi = np.vectorize(F_phi)
Finv_r = lambda p: -r0*np.log(1-p)+K
Finv_r = np.vectorize(Finv_r)
Finv_phi = lambda p: opt.newton((lambda x: F_phi(x)-p), p,tol = eps)
Finv_phi = np.vectorize(Finv_phi)
# p = np.arange(0.01,1,0.01)
# plt.plot(Finv_phi(p),p)
# x = np.arange(0,2*np.pi,0.1)
# plt.plot(x, F_phi(x))
# plt.show()
rarr = Finv_r(randarr1)
phiarr = Finv_phi(randarr2)
pos = np.array([[rarr[i]*np.cos(phiarr[i]+alpha*np.log(rarr[i])),rarr[i]*np.sin(phiarr[i]+alpha*np.log(rarr[i])),np.random.normal(0,WITH)] for i in range(len(randarr1))])
v = lambda r: np.sqrt( G*m*F_r(r)/r+ G*M/r)
vel = np.array([[v(rarr[i])*(-np.sin(phiarr[i]+alpha*np.log(rarr[i]))),v(rarr[i])*(np.cos(phiarr[i]+alpha*np.log(rarr[i]))),0] for i in range(len(randarr1))])
col = np.array([[0.75-0.25*np.sin(phiarr[i]),0.75-0.25*np.sin(phiarr[i]+2*np.pi/3),0.75-0.25*np.sin(phiarr[i]-2*np.pi/3)] for i in range(len(randarr1))])
radius = RADIUS*np.ones((num,1))
#mass = m*np.ones((pos.shape[0], 1))
pos2 = np.concatenate((np.array([[0,0,0]]), pos), axis=0)
vel2 = np.concatenate((np.array([[0,0,0]]), vel), axis=0)
mass2 = np.concatenate((M*np.ones((1,1)),m*np.ones((pos.shape[0], 1))), axis=0)
col2 = np.concatenate((np.array([[0.2,0.2,0.2]]), col), axis=0)
radius2 = np.concatenate((np.array([[5*RADIUS]]),radius), axis = 0)
return Bodies(pos2, vel2, mass = mass2, radius=radius2, dt=DT, color = col2)