def simulate(self):
""" Runs the particle simulation. Simulates one time step, dt, of the particle motion.
Calculates the force between each pair of particles and updates particles' motion accordingly
"""
# Main simulation loop
for i in range(self.iterations):
for a in self.particles:
if a.fixed:
continue
ftot = vector(0, 0, 0) # total force acting on particle a
for b in self.particles:
if a.negligible and b.negligible or a == b:
continue
ab = a.pos - b.pos
ftot += ((K_COULOMB * a.charge * b.charge) / mag2(ab)) * versor(ab)
a.vel += ftot / a.mass * self.dt # update velocity and position of a
a.pos += a.vel * self.dt
a.vsphere.pos(a.pos)
if vp:
vp.show(zoom=1.2)
vp.camera.Azimuth(0.1) # rotate camera
def reflection(p, pos):
n = versor(pos)
return np.dot(np.identity(3) - 2 * n * n[:, np.newaxis], p)
if a == 0:
continue # exactly same velocities
b = 2 * np.dot(pos[i] - pos[j], vj - vi)
c = mag(pos[i] - pos[j])**2 - (ri + rj)**2
d = b**2 - 4.0 * a * c
if d < 0:
continue # something wrong; ignore this rare case
deltat = (-b + np.sqrt(d)) / (2.0 * a
) # t-deltat is when they made contact
pos[i] = pos[i] - (p[i] /
mi) * deltat # back up to contact configuration
pos[j] = pos[j] - (p[j] / mj) * deltat
mtot = mi + mj
pcmi = p[i] - ptot * mi / mtot # transform momenta to cm frame
pcmj = p[j] - ptot * mj / mtot
rrel = versor(pos[j] - pos[i])
pcmi = pcmi - 2 * np.dot(pcmi, rrel) * rrel # bounce in cm frame
pcmj = pcmj - 2 * np.dot(pcmj, rrel) * rrel
p[i] = pcmi + ptot * mi / mtot # transform momenta back to lab frame
p[j] = pcmj + ptot * mj / mtot
pos[i] = pos[i] + (p[i] / mi) * deltat # move forward deltat in time
pos[j] = pos[j] + (p[j] / mj) * deltat
# Bounce off the boundary of the torus
for j in range(Natoms):
poscircle[j] = versor(pos[j]) * RingRadius * [1, 1, 0]
outside = np.greater_equal(mag(poscircle - pos), RingThickness - 2 * Ratom)
for k in range(len(outside)):
if outside[k] == 1 and np.dot(p[k], pos[k] - poscircle[k]) > 0:
p[k] = reflection(p[k], pos[k] - poscircle[k])
gamma * x_dot_m[k])
y_dot[k] -= Dt * (Ks * (bob_y_m[k] - bob_y_m[k - 1]) * factor +
gamma * y_dot_m[k] + g)
for k in range(1, N):
factor = fctr(dij_m[k + 1])
x_dot[k] -= Dt * Ks * (bob_x_m[k] - bob_x_m[k + 1]) * factor
y_dot[k] -= Dt * Ks * (bob_y_m[k] - bob_y_m[k + 1]) * factor
# Check to see if they are colliding
for i in range(1, N):
for j in range(i + 1, N + 1):
dist2 = (bob_x[i] - bob_x[j])**2 + (bob_y[i] - bob_y[j])**2
if dist2 < DiaSq: # are colliding
Ddist = np.sqrt(dist2) - 2 * R
tau = versor([bob_x[j] - bob_x[i], bob_y[j] - bob_y[i], 0])
DR = Ddist / 2 * tau
bob_x[i] += DR[0] # DR.x
bob_y[i] += DR[1] # DR.y
bob_x[j] -= DR[0] # DR.x
bob_y[j] -= DR[1] # DR.y
Vji = vector(x_dot[j] - x_dot[i], y_dot[j] - y_dot[i])
DV = np.dot(Vji, tau) * tau
x_dot[i] += DV[0] # DV.x
y_dot[i] += DV[1] # DV.y
x_dot[j] -= DV[0] # DV.x
y_dot[j] -= DV[1] # DV.y
# Update the loations of the bobs and the stretching of the springs
for k in range(1, N + 1):
bob[k].pos([bob_x[k], bob_y[k], 0])
