def inelastic_particles(particle0: Particle, particle1: Particle, dt: float):
"""
TODO extending for moveable walls
Determines the resulting velocity of a set of colliding particles with mid-fram correction
:param particle0: First particle in the collision
:param particle1: Second particle in the collision
"""
# Determine mass ratios
mass_ratio0 = 2 * particle1.mole.mass / (particle0.mole.mass + particle1.mole.mass)
mass_ratio1 = 2 * particle0.mole.mass / (particle0.mole.mass + particle1.mole.mass)
# generate relative terms
X = particle0.x - particle1.x
U = particle1.u - particle0.u
R = particle0.mole.radius + particle1.mole.radius
a = np.dot(U, U)
b = 2*np.dot(X, U)
c = np.dot(X, X) - R*R
# Determine time of collision
dt0 = (-b + np.sqrt(b*b - 4*a*c))/(2*a)
x0 = particle0.x - particle0.u*dt0
x1 = particle1.x - particle1.u*dt0
u0 = particle0.u
u1 = particle1.u
# Direction magnitude
dir_mag = np.dot(u0 - u1, x0 - x1) / (np.dot(x0 - x1, x0 - x1))
dir_vec = (x0 - x1)
# Set new velocities
particle0.u -= mass_ratio0 * dir_mag * dir_vec
particle1.u -= mass_ratio1 * dir_mag * -dir_vec
# Correct positions
particle0.x = x0 + particle0.u * dt0
particle1.x = x1 + particle1.u * dt0
def inelastic_wall(wall: Wall, particle: Particle, dt: float):
"""
TODO extending for moveable walls
Determines the resulting velocity of a particle bouncing off a wall, with mid-frame position correction
:param wall: the wall object that may intersect the particle
:param particle: the particle in the vicinity of the wall
:param dt: length of the timestep
:return: Boolean value of true if a collision occured
"""
x0 = particle.x
u0 = particle.u
x1 = wall.vert[0, :]
p = x0 - x1
r = particle.mole.radius
unit = wall.unit
norm = wall.norm
dis = np.dot(p, norm)
# Determine if a collision actually occured
if dis > r:
return False
#if norm_dir > 0:
# return False
# Decompose particles velocity normal and tangential to wall
norm_dir = np.dot(u0, norm)
nu = np.multiply(norm_dir, norm)
uu = np.multiply(np.dot(u0, unit), unit)
# Update velocity and position
x0 -= u0 * dt
dt0 = (np.abs(np.dot(x0 - x1, norm)) - r) / np.linalg.norm(nu)
x0 += u0 * dt0
particle.u = uu - nu
particle.x = x0 + particle.u*(dt - dt0)
return True
