top_direction.pos = -sys[:,2] * top_direction.height / 2.0 - offset
top_axis.axis = sys[:,1] * top_axis.height
top_body.axis = sys[:,1] * top_body.height
top_direction.axis = sys[:,2] * top_direction.height
top_trail.append(pos = -offset * 2)
display(width = 800, height = 600)
theta = pi / 12.0
dt = 0.002
sys = np.matrix(np.identity(3))
omega_p = uy * 20
sys = sys.rotate(theta * -uz)
omega_p = omega_p.rotate(theta, -uz)
top = cylinder(radius = 5, height = 0.5, mass = 5)
top_axis = cylinder(radius = 0.25, height = 10)
top_direction = cylinder(radius = 0.27, height = 11, color = color.red)
top_trail = curve(color = color.red)
axes = cylinder_principal_axes(top.mass, 2.5, 5)
# Optional code to provide initial angular velocity to cancel out nutations
omega_precession = top.mass * 9.8 * (top_axis.height / 2) / (axes[1] * mag(omega_p)) * uy
# omega_p += omega_precession
arrow_offset = vector(-12, 0, 0)
omega_axis = arrow(pos = arrow_offset + uy * 4, shaftwidth = 0,
color = color.yellow, opacity = 1)
omega_axis = arrow(pos = vector(-8, -8, -8), shaftwidth = 0,
color = color.yellow, opacity = 1)
l_axis = arrow(pos = vector(-8, -10, -8), shaftwidth = 0,
color = color.green, opacity = 1)
while True:
# Convert omega-prime to omega
omega = (sys.I * omega_p.mat()).vec()
# Update omega from Euler's equations
torque = vector()
omega += delta_omega(axes, omega, torque) * dt
# Calculate l-prime from omega and compensate angular velocity
l = (sys * (inertia_tensor(axes) * omega.mat())).vec()
# Convert omega back to omega-prime
omega_p = (sys * omega.mat()).vec()
# Rotate coordinate system by omega-prime
sys = sys.rotate(omega_p * dt)
# Rotate object to match coordinate system
orient_top(top, top_axis, top_direction, sys)
# Update diagnostics
omega_axis.axis = norm(omega_p) * 3
l_axis.axis = norm(l) * 3
rate(300)