def oderhs(t,z, args = (9.81, 628.32, 1000.)): g,w0,F_a = args n = int((len(z)-4)/5) dz = array(zeros(len(z))) ind = Index(n) ring_state = r_[z[ind.x():ind.y()+1], z[ind.xdot():ind.ydot()+1]] F_x = 0 F_y = F_a for j in xrange(0,n): rhs, F_xj, F_yj = rhs_ball(r_[z[ind.r(j):ind.theta(j)+1], z[ind.rdot(j):ind.phidot(j)+1]], ring_state, args = (g,w0)) F_x += F_xj F_y += F_yj dz[ind.r(j)] = z[ind.rdot(j)] dz[ind.theta(j)] = z[ind.thetadot(j)] dz[ind.rdot(j):ind.phidot(j)+1] = rhs dz[ind.x():ind.y()+1] = z[ind.xdot():ind.ydot()+1] dz[ind.xdot()] = F_x/m0 dz[ind.ydot()] = F_y/m0 return dz
return rhs ## Initial position/motion of the rolling elements n = 8 N = 5*n+4 u0 = array(zeros(N)) ind = Index(n) # This is rand(8)*1e-6: perturbation = array([ 9.78702856e-07, 2.93684668e-07, 4.79000309e-07, 3.21827339e-07, 8.01445882e-07, 7.26611584e-08, 8.74822963e-08, 7.41679693e-07]) for i in xrange(0,n): u0[ind.r(i)] = (b0+c0)/2 + perturbation[i] #rand()*1e-6 # r u0[ind.theta(i)] = -pi/2 + 2*pi*i/n# theta u0[ind.rdot(i)] = 0 # rdot u0[ind.thetadot(i)] = 0*b0/(b0+c0)#*w0 # thetadot u0[ind.phidot(i)] = 0*b0/2/a0*628.32 # phidot - note that phi is not a state variable since it does not matter here end_state = array([9.81, 628.32, 1000.]) h = 1. / numpy.max(end_state) #rhs_ = Sjoe((0,0,0)) #rhs = Sjoe(10*h*end_state) rhs_ = Sjoe((0.0981,0,0)) def f(u): return rhs_(0,u) A0 = jac(f,u0) uk = copy(u0) #
def rhs(t,y):
return oderhs(t,y)
rhs.name = 'rhs'
return rhs
#Sjoe.name = 'Sjoe'
## Initial position/motion of the rolling elements
n = 8
N = 5*n+4
u0 = array(zeros(N))
ind = Index(n)
for i in xrange(0,n):
u0[ind.r(i)] = (b0+c0)/2 # r
u0[ind.theta(i)] = -pi/2 + 2*pi*i/n# theta
u0[ind.rdot(i)] = 0 # rdot
u0[ind.thetadot(i)] = b0/(b0+c0)*w0 # thetadot
u0[ind.phidot(i)] = b0/2/a0*w0 # phidot - note that phi is not a state variable since it does not matter here
rhs = Sjoe()
cv=IVP.CVode(rhs,u0)
cv.set_method('BDF','Newton')
atol = array(zeros(N))
for i in range(0,N):
atol[i] = 1e-8
cv.set_tolerance(atol,rtol=1.e-8)
numsteps = 100
t0 = 0.005