def poincare_step(z, t):
" Integrate until the poincare section is reached again, in the right direction"
# Integrate just a tiny step to make sure we don't stop at the
# same point
(y, tout, t_root, y_root, i_root, info_dict) = lsodar.odeintr(
f,
copy(z),
linspace(t, t + t_small, np2),
rtol=rtol,
atol=atol,
full_output=1,
root_func=event,
root_term=array([0]),
)
ynew = copy(y[-1, :])
tnew = copy(tout[-1])
print tnew
# Main integration
(y, tout, t_root, y_root, i_root, info_dict) = lsodar.odeintr(
f,
copy(ynew),
linspace(tnew, tnew + max_t, np),
rtol=rtol,
atol=atol,
full_output=1,
root_func=event,
root_term=array([1]),
)
ynew = copy(y[-1, :])
if tout[-1] == tnew + max_t:
raise RuntimeError, ("Never reached the Poincare section again. Oh noes!", ynew)
tnew = copy(tout[-1])
print tnew
# Must check that the trajectory is going the right way
if dot(f(ynew, tnew), n) < 0:
print "Reached wrong side of the hyperplane, continuing..."
# The solution cannot pass the hyperplane in the same direction two
# times in a row, so just integrate one more time
(y, tout, t_root, y_root, i_root, info_dict) = lsodar.odeintr(
f,
copy(ynew),
linspace(tnew, tnew + max_t, np),
rtol=rtol,
atol=atol,
full_output=1,
root_func=event,
root_term=array([1]),
)
ynew = copy(y[-1, :])
tnew = copy(tout[-1])
print tnew
if len(t_root) == 0:
raise RuntimeError, ("Never reached the Poincare section again. Oh noes!", ynew)
else:
print "Reached Poincare section again at", ynew
return (ynew, tnew)
y0[5*i] = (b0+c0)/2 # r
y0[5*i+1] = 2*pi*i/n # theta
y0[5*i+2] = 0 # rdot
y0[5*i+3] = b0/(b0+c0)*w0 # thetadot
y0[5*i+4] = b0/2/a0*w0 # phidot - note that phi is not a state variable since it does not matter here
#numsteps = 2000
numsteps = 1000
start = 0
end = 0.03
T = linspace(start,end,numsteps)
(Y, info) = lsodar.odeintr(oderhs, copy(y0), T, atol = 1e-8, rtol = 1e-8, full_output=1)
print Y[-1,:]
for j in xrange(0,n):
subplot(n+1,5,5*j+1)
plot(T, Y[:,5*j+0]) #r
subplot(n+1,5,5*j+2)
plot(T, Y[:,5*j+1]) #th
subplot(n+1,5,5*j+3)
plot(T, Y[:,5*j+2]) # rdot
subplot(n+1,5,5*j+4)
plot(T, Y[:,5*j+3]) # thdot
