#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright (C) 2010 Modelon AB
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, version 3 of the License.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
from scipy import *
import pylab as P
import nose
from assimulo.problem import Explicit_Problem
from assimulo.solvers import CVode
[docs]def run_example(with_plots=True):
"""
Simulations for the Gyro (Heavy Top) example in Celledoni/Safstrom:
Journal of Physics A, Vol 39, 5463-5478, 2006
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
def curl(v):
return array([[0,v[2],-v[1]],[-v[2],0,v[0]],[v[1],-v[0],0]])
#Defines the rhs
def f(t,u):
"""
Simulations for the Gyro (Heavy Top) example in Celledoni/Safstrom:
Journal of Physics A, Vol 39, 5463-5478, 2006
"""
I1=1000.
I2=5000.
I3=6000.
u0=[0,0,1.]
pi=u[0:3]
Q=(u[3:12]).reshape((3,3))
Qu0=dot(Q,u0)
f=array([Qu0[1],-Qu0[0],0.])
f=0
omega=array([pi[0]/I1,pi[1]/I2,pi[2]/I3])
pid=dot(curl(omega),pi)+f
Qd=dot(curl(omega),Q)
return hstack([pid,Qd.reshape((9,))])
def energi(state):
energi=[]
for st in state:
Q=(st[3:12]).reshape((3,3))
pi=st[0:3]
u0=[0,0,1.]
Qu0=dot(Q,u0)
V=Qu0[2] # potential energy
T=0.5*(pi[0]**2/1000.+pi[1]**2/5000.+pi[2]**2/6000.)
energi.append([T])
return energi
#Initial conditions
y0=hstack([[1000.*10,5000.*10,6000*10],eye(3).reshape((9,))])
#Create an Assimulo explicit problem
exp_mod = Explicit_Problem(f,y0, name="Gyroscope Example")
#Create an Assimulo explicit solver (CVode)
exp_sim=CVode(exp_mod)
#Sets the parameters
exp_sim.discr='BDF'
exp_sim.iter='Newton'
exp_sim.maxord=2 #Sets the maxorder
exp_sim.atol=1.e-10
exp_sim.rtol=1.e-10
#Simulate
t, y = exp_sim.simulate(0.1)
#Basic tests
nose.tools.assert_almost_equal(y[-1][0],692.800241862)
nose.tools.assert_almost_equal(y[-1][8],7.08468221e-1)
#Plot
if with_plots:
P.plot(t,y/10000.)
P.xlabel('Time')
P.ylabel('States, scaled by $10^4$')
P.title(exp_mod.name)
P.show()
return exp_mod, exp_sim
if __name__=='__main__':
mod,sim = run_example()