Newton Cradle Example

Author:Alex Dumitrache (alex@cimr.pub.ro) Date:2010/05/05

This is an interactive example of Newton’s Cradle.

For a simplified version, see the ODEDynamics: Newton Ball Experiment tutorial.

Here is the code:

# Newton's Cradle

# First, some useful functions
def rx(ang):
    return mat3(1).rotate(ang, (1,0,0))
def ry(ang):
    return mat3(1).rotate(ang, (0,1,0))
def rz(ang):
    return mat3(1).rotate(ang, (0,0,1))

def remove(objs):
    objs = worldObjects(objs)

    for o in objs:
        for c in o.iterChilds():
            remove(c)
        for s in getScene().items:
            if type(s) == ODEDynamics:
                try: s.remove(o)
                except: pass
            if type(s) == cgkit._core.WorldObject:
                try: s.removeChild(o)
                except: pass

# Adjust contact properties and simulation parameters
defaultContactProps = ODEContactProperties(bounce = 1, mu = 1, soft_erp=0.5, soft_cfm=1E-10)
odeSim = ODEDynamics( gravity=9.81, substeps=20, defaultcontactproperties = defaultContactProps, use_quick_step = False)

# Define materials
matRed     = GLMaterial(name="Red",     diffuse=(1,0,0))
matGreen   = GLMaterial(name="Green",   diffuse=(0,1,0))
matBlue    = GLMaterial(name="Blue",    diffuse=(0,0,1))
matCyan    = GLMaterial(name="Cyan",    diffuse=(0,1,1))
matMagenta = GLMaterial(name="Magenta", diffuse=(1,0,1))
matYellow  = GLMaterial(name="Yellow",  diffuse=(1,1,0))
matOrange  = GLMaterial(name="Orange",  diffuse=(1,0.5,0))
matWhite   = GLMaterial(name="White",   diffuse=(1,1,1))
matGray    = GLMaterial(name="Gray",    diffuse=(0.5,0.5,0.5))
matBlack   = GLMaterial(name="Black",   diffuse=(0,0,0))
materials  = [matRed, matGreen, matBlue, matCyan, matYellow, matOrange, matMagenta, matWhite, matGray, matBlack]

# The cradle is made of balls, pins and hinge joints
balls = []; pins = []; hinges = []
def createNewCradle(n):
    global balls, pins, hinges

    print "Creating a cradle with %d balls..." % n

    # Remove existing objects from the scene and create the cradle from scratch
    remove(balls + pins + hinges)
    balls = []; pins = []; hinges = []

    # Create 'n' balls and pins, then connect them with hinge joints
    for i in range(n):
        x = (i-n/2.0) * 0.2
        balls.append(Sphere(radius = 0.1, pos = (x, 0, 0), mass = 1, material = materials[i]))
        pins.append(CCylinder(radius = 0.01, length = 0.2, rot = rx(pi/2), pos = (x, 0, 1), mass = 1, material = materials[i]))
        hinges.append(ODEHingeJoint("Hinge 1", pins[-1], balls[-1], pos = pins[-1].pos, rot = rz(pi/2)))

    # Add the bodies to the simulation, and then add the joints
    odeSim.add(balls + pins)
    odeSim.add(hinges)

    # Add Box decorations for each ball (only for rendering, do not add them to ODEDynamics)
    for i, s in enumerate(balls):
        x = (i-n/2.0) * 0.2
        b = Box(pos = (x, 0, 0.5), lx = 0.005, ly = 0.1, lz = 1, material=materials[i])
        link(b, s)

    # Fix all the pins here
    for p in pins:
        p.manip.odebody.setKinematic()

# By default, create a cradle with 4 balls
createNewCradle(4)

# Key press handler
def onKeyPress(K):
    if K.key > '0' and K.key <= '9':
        createNewCradle(int(K.key))
    if K.key.lower() == 'h':
        balls[0].manip.addForce((-100,0,0))
    if K.key.lower() == 'r':
        eventmanager.event(RESET)

eventmanager.connect(KEY_PRESS, onKeyPress)

print """
Press H to apply an impulse to the red ball
Press R to restart the simulation
Press 1...9 to change the number of balls
"""

# That's it :)

Download the script and run it using:

> python viewer.py newton-cradle.py

Apply an impulse to the red balls with H key, change the number of balls with 1 ... 9 and reset the simulation with R.

Now let’s break the code into pieces:

• First, we define some useful functions:

  • rx, ry and rz are elementary rotations
  • remove will clean up the scene and allow us to regenerate the cradle from scratch

• Then, the contact properties are defined.

  • The most important is bounce = 1.
  • Also, you have to set mu=1, although in real physics, mu should not have any influence.

• ODEDynamics parameters:

  • substeps is also important here. For best results, set it to high values.
  • cfm and erp are not very important, so you may also stick with the defaults here.

• Materials: it is a list of GLMaterial objects; one color for each ball.

• createNewCradle(n):

  The cradle contains n balls, each ball being connected to a fixed pin using a hinge joint.

  Steps for creating a new cradle:

  • Remove previous cradle from the scene
  • Create n balls, pins and hinge joints between each ball-pin pair
  • Add the bodies and the joints to the ODEDynamics component
  • Create n boxes, which will show the links between each ball and pin
  • Use the boxes only for rendering, and attach them to the balls using cgkit function link
  • Lock the position of the pins by setting the kinematic state flag for them

• By default, create a cradle with 4 balls

• Add a handler for keyboard events (keys H, R and 1 ... 9)

• Don’t forget to display a short usage help :)

Whew!