Bouncing

from vegesvgplot import *

g = 9.81
m = 5.0
dE = -1.0


def PrintTime(t):

  print 'At t = %gs,' % (t)


def PrintState(x, v):

  Eg = m * g * x[1]
  Ek = 0.5 * m * VLengthSquared(v)
  E = Eg + Ek

  print '  x = ' + GFTupleStr(x) + 'm'
  print '  v = ' + GFTupleStr(v) + 'm/s'
  print '  Eg = %gJ' % (Eg)
  print '  Ek = %gJ' % (Ek)
  print '  E = %gJ' % (E)


def Bounce(x, v):

  Eg = m * g * x[1]
  Ek = 0.5 * m * VLengthSquared(v)
  E1 = Eg + Ek
  E2 = max(0, E1 + dE)

  v1 = (v[0], -v[1])
  v2 = VScaled(v1, sqrt(E2) / sqrt(E1))

  return x, v2


def Main():

  x0 = (0.0, 10.0)
  v0 = (20.0, 0.0)

  t = 0.0
  x = x0
  v = v0
  Eg = m * g * x[1]
  Ek = 0.5 * m * VLengthSquared(v)
  E = Eg + Ek

  NumBounces = 0

  PrintTime(t)
  PrintState(x, v)

  dt = sqrt(2.0 * x[1] / g)

  t += dt
  x = (x[0] + dt * v[0], 0.0)
  v = (v[0], v[1] - g * dt)
  t1 = t

  while v[1] < 0:

    PrintTime(t)
    PrintState(x, v)

    x, v = Bounce(x, v)

    if v[1] > 0.0:

      NumBounces += 1
      print 'Bounce %d:' % (NumBounces)

      PrintState(x, v)

      #Advance to instant before next bounce
      dt = 2.0 * v[1] / g
      x = (x[0] + dt * v[0], 0.0)
      v = (v[0], -v[1])

      t += dt

      print '%gs later...' % (dt)


    else:

      print 'Splat!'
      PrintState(x, v)
      print

  print 'End of simulation\n'

  print 'Mass of ball: %gkg' % (m)
  print 'g = %gm/s/s (downward)' % (g)

  print 'Initial state:'
  PrintState(x0, v0)

  print 'Duration of initial fall: %gs' % (t1)
  print 'Number of bounces:', NumBounces
  print 'Duration of fall and bouncing: %gs' % (t)


Main()