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calculate.py
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calculate.py
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import math
import numpy as np
show = True
# Constants ####################################################################
g = 9.81
m = 0.005
R = 0.1
L = 2*R
Ig = 1/12 * m * L**2
I0 = Ig + m * R**2
ue = 0.3
uc = 0.2
# Simulation parameters ########################################################
output_file = "temp.txt"
dt = 0.001
theta0 = math.pi/2 - 0.1
dtheta0 = 0
# Start file ###################################################################
file = open(output_file, 'w')
file.write("# Constants\n")
file.write("g = %f\n" % g)
file.write("m = %f\n" % m)
file.write("R = %f\n" % R)
file.write("L = %f\n" % L)
file.write("Ig = %f\n" % Ig)
file.write("I0 = %f\n" % I0)
file.write("ue = %f\n" % ue)
file.write("uc = %f\n" % uc)
file.write("\n# Simulation parameters\n")
file.write("dt = %f\n" % dt)
file.write("dtheta0 = %f\n" % dtheta0)
# General functions ############################################################
def integrate(dt, x, dx):
return x+dx*dt
def rk4(cte, dt, X0, f):
X0 = np.array(X0)
k1 = dt*f(*cte, X0)
k2 = dt*f(*cte, X0+k1/2.)
k3 = dt*f(*cte, X0+k2/2.)
k4 = dt*f(*cte, X0+k3)
X = X0 + (k1+2*k2+2*k3+k4)/6.
return X
def y_calc(R, theta):
return R*math.sin(theta)
def dy_calc(R, theta, dtheta):
return R*dtheta*math.cos(theta)
def ddy_calc(R, theta, dtheta, ddtheta):
return R*(ddtheta*math.cos(theta)-dtheta**2*math.sin(theta))
def pos_calc(R, theta, x, y):
dx = R*math.cos(theta)
dy = R*math.sin(theta)
return x-dx, x+dx, y-dy, y+dy
# No slip functions ############################################################
def ii_noslip(dtheta, ddtheta):
if (dtheta<0 or (dtheta==0 and ddtheta<0)):
return 1
else:
return -1
def f_noslip(g, m, R, I0, X):
theta = X[0]
dtheta = X[1]
x = X[2]
return np.array([dtheta, -m*g*R/I0*math.cos(theta), -R*dtheta*math.sin(theta)])
def ddtheta_noslip(g, m, R, I0, theta):
return -m*g*R/I0 * math.cos(theta)
def check_noslip(g, R, ue, theta, dtheta, ddtheta, ii):
return not( ii*ddtheta >= -ii*(dtheta**2*math.cos(theta)+ue*(g/R-dtheta**2*math.sin(theta))*ii)/
(math.sin(theta)+ue*math.cos(theta)*ii) )
def N_noslip(g, m, R, theta, dtheta, ddtheta):
return m*(g+R*(ddtheta*math.cos(theta)-dtheta**2*math.sin(theta)))
def x_noslip(R, dtheta):
return R*math.cos(theta)
def dx_noslip(R, theta, dtheta):
return -R*dtheta*math.sin(theta)
def ddx_noslip(R, theta, dtheta, ddtheta):
return -R*(ddtheta*math.sin(theta)+dtheta**2*math.cos(theta))
# Slip functions ###############################################################
def f_slip(g, m, R, Ig, uc, ii, X):
theta = X[0]
dtheta = X[1]
x = X[2]
dx = X[3]
return np.array([dtheta, (dtheta**2*math.sin(theta)-g/R)*(math.cos(theta)-uc*math.sin(theta)*ii)/
(math.cos(theta)*(math.cos(theta)-uc*math.sin(theta)*ii)+Ig/(m*R**2)),
dx, uc*ii*m*(g+R*(ddtheta*math.cos(theta)-dtheta**2*math.sin(theta)))])
def ddtheta_slip(g, m, R, Ig, theta, dtheta, ii):
return ( (dtheta**2*math.sin(theta)-g/R)*(math.cos(theta)-uc*math.sin(theta)*ii)/
(math.cos(theta)*(math.cos(theta)-uc*math.sin(theta)*ii)+Ig/(m*R**2)) )
def N_slip(g, m, R, theta, dtheta, ddtheta):
return m*(g+R*(ddtheta*math.cos(theta)-dtheta**2*math.sin(theta)))
def ddx_slip(uc, N, ii):
return uc*N*ii
def check_slip(R, theta, dtheta, dx, ii):
return ii*dx < -dtheta*R*math.sin(theta)
def ii_slip(R, theta, dtheta, dx):
if dx <= -dtheta*R*math.sin(theta):
return 1
else:
return -1
# Simulation ###################################################################
t = 0
theta = theta0
dtheta = dtheta0
# Calculate if slip (assuming no slip)
ddtheta = ddtheta_noslip(g, m, R, I0, theta)
N = N_noslip(g, m, R, theta, dtheta, ddtheta)
ddx = ddx_noslip(R, theta, dtheta, ddtheta)
dx = dx_noslip(R, theta, dtheta)
x = x_noslip(R, theta)
ddy = ddy_calc(R, theta, dtheta, ddtheta)
dy = dy_calc(R, theta, dtheta)
y = y_calc(R, theta)
ii = ii_noslip(dtheta, ddtheta)
slip = check_noslip(g, R, ue, theta, dtheta, ddtheta, ii)
x1, x2, y1, y2 = pos_calc(R, theta, x, y)
if show:
print(t, slip, ii, N, theta, dtheta, ddtheta, x, dx, ddx, y, dy, ddy, x1, y1, x2, y2)
file.write("\n# Simulation data\n")
file.write("# t \t slip \t ii \t N \t theta \t dtheta \t ddtheta \t x \t dx \t ddx \t y \t dy \t ddy \t x1 \t y1 \t x2 \t y2\n")
file.write("%f %d %d %f %f %f %f %f %f %f %f %f %f %f %f %f %f\n" %
(t, slip, ii, N, theta, dtheta, ddtheta, x, dx, ddx, y, dy, ddy, x1, y1, x2, y2))
while y>0:
if not slip:
ii = ii_noslip(dtheta, ddtheta)
theta, dtheta, x = rk4([g, m, R, I0], dt, [theta, dtheta, x], f_noslip)
ddtheta = ddtheta_noslip(g, m, R, I0, theta)
ddx = ddx_noslip(R, theta, dtheta, ddtheta)
dx = dx_noslip(R, theta, dtheta)
N = N_noslip(g, m, R, theta, dtheta, ddtheta)
ddy = ddy_calc(R, theta, dtheta, ddtheta)
dy = dy_calc(R, theta, dtheta)
y = y_calc(R, theta)
slip = check_noslip(g, R, ue, theta, dtheta, ddtheta, ii)
else:
ii = ii_slip(R, theta, dtheta, dx)
theta, dtheta, x, dx = rk4([g, m, R, Ig, uc, ii], dt, [theta, dtheta, x, dx], f_slip)
ddtheta = ddtheta_noslip(g, m, R, I0, theta)
ddx = ddx_slip(uc, N, ii)
N = N_slip(g, m, R, theta, dtheta, ddtheta)
ddy = ddy_calc(R, theta, dtheta, ddtheta)
dy = dy_calc(R, theta, dtheta)
y = y_calc(R, theta)
slip = check_slip(R, theta, dtheta, dx, ii)
x1, x2, y1, y2 = pos_calc(R, theta, x, y)
t += dt
if show:
print(t, slip, ii, N, theta, dtheta, ddtheta, x, dx, ddx, y, dy, ddy, x1, y1, x2, y2)
file.write("%f %d %d %f %f %f %f %f %f %f %f %f %f %f %f %f %f\n" %
(t, slip, ii, N, theta, dtheta, ddtheta, x, dx, ddx, y, dy, ddy, x1, y1, x2, y2))
#input()
file.close()
print("end")