from math import sin, cos
class beads2d(object):
"""Vector field that describes the approximation of the Beads problem."""
def __init__(self):
pass
# Samples the vector field of the Beads problem
def sample(self, x, y, t):
u = -2 * y + (2 * sin(t)) / 3
v = +2 * x - (2 * cos(t)) / 3
return u, v;
# Samples the x-partial of the vector field of the Beads problem
def sample_dx(self, x, y, t):
u = 0
v = 2
return u, v;
# Samples the y-partial of the vector field of the Beads problem
def sample_dy(self, x, y, t):
u = -2
v = 0
return u, v;
# Samples the t-partial of the vector field of the Beads problem
def sample_dt(self, x, y, t):
u = (2 * cos(t)) / 3
v = (2 * sin(t)) / 3
return u, v;