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#
# MIT No Attribution
#
# Copyright (C) 2010-2023 Joel Andersson, Joris Gillis, Moritz Diehl, KU Leuven.
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this
# software and associated documentation files (the "Software"), to deal in the Software
# without restriction, including without limitation the rights to use, copy, modify,
# merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
# permit persons to whom the Software is furnished to do so.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
# INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
# PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
# HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
# OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
#
#
from casadi import *
import pylab as plt
# Height and velocity of ball
h = SX.sym('h')
v = SX.sym('v')
x = vertcat(h, v)
# ODE right-hand-side
hdot = v
vdot = -9.81
xdot = vertcat(hdot, vdot)
# Event indicator, trigger when it becomes negative
event_indicator = h
# DAE problem structure, with zero-crossing output
dae = dict(x = x, ode = xdot, zero = event_indicator)
# Event transition function
post_x = vertcat(h, -0.8*v)
transition = Function('transition', dict(x = x, post_x = post_x),
event_in(), event_out())
# Create an integrator instance for integrating over 7s
tgrid = np.linspace(0, 7, 100)
sim = integrator('sim', 'cvodes', dae, 0, tgrid,
dict(transition = transition))
# Simulate with initial height of 5
x0 = [5, 0]
simres = sim(x0 = x0)
# Visualize the solution
plt.figure(1)
plt.clf()
plt.plot(tgrid, simres['xf'][0, :].T)
plt.grid()
plt.show()
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