# from sage.calculus.desolvers import desolve_odeint
x,y=var('x,y')
mu=-0.8
f=[mu+x*x,-y]
p1=plot_vector_field(f,(x,-2,2),(y,-2,2))
sol=desolve_odeint(f,[-1.5,1],srange(0,10,0.1),[x,y])
p2=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[-sqrt(-mu),2],srange(0,10,0.1),[x,y])
p3=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[-mu/2,1],srange(0,10,0.1),[x,y])
p4=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[sqrt(-mu)+0.1,1],srange(0,1,0.1),[x,y])
p5=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[sqrt(-mu),2],srange(0,10,0.1),[x,y])
p6=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[mu/2,1],srange(0,10,0.1),[x,y])
p7=line(zip(sol[:,0],sol[:,1]))
show(p1+p2+p3+p4+p5+p6+p7)
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# voorbeeld cursus pagina 114
from sage.calculus.desolvers import desolve_odeint
x,y=var('x,y')
mu=0
f=[mu+x*x,-y]
p1=plot_vector_field(f,(x,-4,4),(y,-2,2))
sol=desolve_odeint(f,[-3,2],srange(0,5,0.1),[x,y])
p2=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[-2.5,2],srange(0,7.5,0.1),[x,y])
p3=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[0.1,2],srange(0,7.5,0.1),[x,y])
p4=line(zip(sol[:,0],sol[:,1]))
show(p1+p2+p3+p4)
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# voorbeeld cursus pagina 114
from sage.calculus.desolvers import desolve_odeint
x,y=var('x,y')
mu=1
f=[mu+x*x,-y]
p1=plot_vector_field(f,(x,-4,4),(y,-2,2))
sol=desolve_odeint(f,[-3,2],srange(0,2.5,0.1),[x,y])
p2=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[-2.5,1],srange(0,2.5,0.1),[x,y])
p3=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[-2,-2],srange(0,2.5,0.1),[x,y])
p4=line(zip(sol[:,0],sol[:,1]))
show(p1+p2+p3+p4)
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# inzoomend op het stabiele knooppunt voor mu<0
# raken de fasebanen aan de x-as of de y-as. De trage richting wordt bepaald door min(1,2*sqrt(-mu))
x,y=var('x,y')
mu=-0.3 # er is een verandering merkbaar bij mu=-0.25
f=[mu+x*x,-y]
p1=plot_vector_field(f,(x,-sqrt(-mu)-0.01,-sqrt(-mu)+0.01),(y,-0.01,0.01))
sol=desolve_odeint(f,[-sqrt(-mu)-0.005,0.01],srange(0,10,0.1),[x,y])
p2=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[-sqrt(-mu),0.01],srange(0,10,0.1),[x,y])
p3=line(zip(sol[:,0],sol[:,1]))
sol=desolve_odeint(f,[-sqrt(-mu)+0.01,0.01],srange(0,10,0.1),[x,y])
p4=line(zip(sol[:,0],sol[:,1]))
show(p1+p2+p3+p4)
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