vedo/examples/simulations/gyroscope1.py

"""Simulation of a gyroscope hanging from a spring"""
# (adapted by M. Musy from Bruce Sherwood, 2009)
from vedo import *

# ############################################################ parameters
dt = 0.005  # time step
ks = 15     # spring stiffness
Lrest = 1   # unstretched length of spring
Ls = 1      # length of gyroscope shaft
M = 1       # mass of gyroscope (massless shaft)
R = 0.4     # radius of gyroscope rotor
omega = 50  # angular velocity of rotor (rad/s, not shown)
gpos = vector(0, 0, 0)  # initial position of spring free end

# ############################################################ inits
top = vector(0, 2, 0)       # where top of spring is held
precess = vector(0, 0, 0)   # initial momentum of center of mass
Fgrav = vector(0, -M * 9.81, 0)
gaxis = vector(0, 0, 1)     # initial orientation of gyroscope
gaxis = versor(gaxis)
I = 1 / 2 * M * R ** 2      # moment of inertia of gyroscope
Lrot = I * omega * gaxis    # angular momentum
cm = gpos + 0.5 * Ls * gaxis  # center of mass of shaft

# ############################################################ the scene
plt = Plotter()
plt += __doc__

shaft = Cylinder([[0, 0, 0], Ls * gaxis], r=0.03).c("dark green")
rotor = Cylinder([(Ls - 0.55) * gaxis, (Ls - 0.45) * gaxis], r=R).c("tomato")
gyro = shaft + rotor   # group meshes into a single one of type Assembly

spring = Spring(top, gpos, r1=0.06, thickness=0.01).c("gray")
plt += [gyro, spring]       # add it to Plotter.
plt += Box(top, size=(0.2, 0.02, 0.2)).c("gray")
plt += Box(pos=(0, 0.5, 0), size=(2.6, 3, 2.6)).wireframe().c("gray",0.2)

# ############################################################ the physics
def loop_func(event):
    global  t, Lrot, precess, cm, gpos
    t += dt
    Fspring = -ks * versor(gpos - top) * (mag(gpos - top) - Lrest)
    torque = cross(-1/2 * Ls * versor(Lrot), Fspring)  # torque about center of mass
    Lrot += torque * dt
    precess += (Fgrav + Fspring) * dt  # momentum of center of mass
    cm += (precess / M) * dt
    gpos = cm - 1/2 * Ls * versor(Lrot)

    # set orientation along gaxis and rotate it around its axis by omega*t degrees
    gyro.reorient([0,0,1], Lrot, rotation=omega*t, rad=True).pos(gpos)
    spring = Spring(top, gpos, r1=0.06, thickness=0.01).c("gray")
    plt.remove("Spring").add(spring)
    plt.render()

t = 0
plt.add_callback("timer", loop_func)
plt.timer_callback("start")
plt.show().close()