:orphan:

pendulum3
---------


3D animation of a pendulum

.. raw:: html

  <video width="558" height="558" controls autoplay>
    <source src="../_static/examples/pendulum3.mov" type="video/mp4">
    <source src="../_static/examples/pendulum3.ogg" type="video/ogg">
  </video>

----

.. code-block:: python
    
    
    
    import numpy as np
    import time
    import gr
    import gr3
    
    try:
        from time import perf_counter
    except ImportError:
        from time import clock as perf_counter
    
    g = 9.8  # gravitational constant
    
    
    def rk4(x, h, y, f):
        k1 = h * f(x, y)
        k2 = h * f(x + 0.5 * h, y + 0.5 * k1)
        k3 = h * f(x + 0.5 * h, y + 0.5 * k2)
        k4 = h * f(x + h, y + k3)
        return x + h, y + (k1 + 2 * (k2 + k3) + k4) / 6.0
    
    
    def damped_pendulum_deriv(t, state):
        theta, omega = state
        return np.array([omega, -gamma * omega - g / L * np.sin(theta)])
    
    
    def sign(x):
        if x > 0:
            return 1
        elif x < 0:
            return -1
        else:
            return 0
    
    
    def pendulum(t, theta, omega, acceleration):
        gr.clearws()
        gr.setviewport(0, 1, 0, 1)
    
        x, y = (np.sin(theta) * 3.0, -np.cos(theta) * 3.0)
    
        gr3.clear()
        # draw pivot point
        gr3.drawspheremesh(1, (0, 0, 0), (0.4, 0.4, 0.4), 0.1)
        # draw rod
        gr3.drawcylindermesh(1, (0, 0, 0), (x, y, 0), (0.6, 0.6, 0.6), 0.05, 3.0)
        # draw sphere
        gr3.drawspheremesh(1, (x, y, 0), (1, 1, 1), 0.25)
        # show angular velocity
        V = 0.3 * omega - sign(omega) * 0.15
        gr3.drawcylindermesh(1, (x, y, 0), (np.cos(theta), np.sin(theta), 0), (0, 0, 1), 0.05, V)
        gr3.drawconemesh(1, (x + np.cos(theta) * V, y + np.sin(theta) * V, 0), (-y, x, 0), (0, 0, 1), 0.1, sign(omega) * 0.25)
        # show angular acceleration
        A = 0.3 * acceleration
        gr3.drawcylindermesh(1, (x, y, 0), (np.sin(theta), np.cos(theta), 0), (1, 0, 0), 0.05, A)
        gr3.drawconemesh(1, (x + np.sin(theta) * A, y + np.cos(theta) * A, 0), (x, -y, 0), (1, 0, 0), 0.1, 0.25)
        # draw GR3 objects
        gr3.drawimage(0, 1, 0.15, 0.85, 500, 350, gr3.GR3_Drawable.GR3_DRAWABLE_GKS)
    
        gr.settextfontprec(2, gr.TEXT_PRECISION_STRING)
        gr.setcharheight(0.024)
        gr.settextcolorind(1)
        gr.textext(0.05, 0.96, 'Damped Pendulum')
        gr.mathtex(0.05, 0.9, '\\omega=\\dot{\\theta}')
        gr.mathtex(0.05, 0.83, '\\dot{\\omega}=-\\gamma\\omega-\\frac{g}{l}sin(\\theta)')
        gr.setcharheight(0.020)
        gr.textext(0.05, 0.20, 't:%7.2f' % t)
        gr.textext(0.05, 0.16, '\\theta:%7.2f' % (theta / np.pi * 180))
        gr.settextcolorind(4)
        gr.textext(0.05, 0.12, '\\omega:%7.2f' % omega)
        gr.settextcolorind(2)
        gr.textext(0.05, 0.08, 'y_{A}:%6.2f' % acceleration)
        gr.updatews()
        return
    
    
    theta = 110.0  # initial angle
    gamma = 0.1  # damping coefficient
    L = 1  # pendulum length
    
    t = 0
    dt = 0.04
    state = np.radians([theta, 0])
    
    gr3.init()
    gr3.setcameraprojectionparameters(45, 1, 100)
    gr3.cameralookat(0, -2, 6, 0, -2, 0, 0, 1, 0)
    gr3.setbackgroundcolor(1, 1, 1, 1)
    gr3.setlightdirection(1, 1, 10)
    
    now = perf_counter()
    
    while t < 30:
        start = now
    
        t, state = rk4(t, dt, state, damped_pendulum_deriv)
        theta, omega = state
        acceleration = np.sqrt(2 * g * L * (1 - np.cos(theta)))
        pendulum(t, theta, omega, acceleration)
    
        now = perf_counter()
        if start + dt > now:
            time.sleep(start + dt - now)
    
    gr3.terminate()