def _EOM_dxdv(x,t,pot):
"""
NAME:
_EOM_dxdv
PURPOSE:
implements the EOM, i.e., the right-hand side of the differential
equation, for integrating phase space differences, rectangular
INPUT:
x - current phase-space position
t - current time
pot - (list of) Potential instance(s)
OUTPUT:
dy/dt
HISTORY:
2011-10-18 - Written - Bovy (NYU)
"""
#x is rectangular so calculate R and phi
R= nu.sqrt(x[0]**2.+x[1]**2.)
phi= nu.arccos(x[0]/R)
sinphi= x[1]/R
cosphi= x[0]/R
if x[1] < 0.: phi= 2.*nu.pi-phi
#calculate forces
Rforce= _evaluateplanarRforces(pot,R,phi=phi,t=t)
phiforce= _evaluateplanarphiforces(pot,R,phi=phi,t=t)
R2deriv= _evaluateplanarPotentials(pot,R,phi=phi,t=t,dR=2)
phi2deriv= _evaluateplanarPotentials(pot,R,phi=phi,t=t,dphi=2)
Rphideriv= _evaluateplanarPotentials(pot,R,phi=phi,t=t,dR=1,dphi=1)
#Calculate derivatives and derivatives+time derivatives
dFxdx= -cosphi**2.*R2deriv\
+2.*cosphi*sinphi/R**2.*phiforce\
+sinphi**2./R*Rforce\
+2.*sinphi*cosphi/R*Rphideriv\
-sinphi**2./R**2.*phi2deriv
dFxdy= -sinphi*cosphi*R2deriv\
+(sinphi**2.-cosphi**2.)/R**2.*phiforce\
-cosphi*sinphi/R*Rforce\
-(cosphi**2.-sinphi**2.)/R*Rphideriv\
+cosphi*sinphi/R**2.*phi2deriv
dFydx= -cosphi*sinphi*R2deriv\
+(sinphi**2.-cosphi**2.)/R**2.*phiforce\
+(sinphi**2.-cosphi**2.)/R*Rphideriv\
-sinphi*cosphi/R*Rforce\
+sinphi*cosphi/R**2.*phi2deriv
dFydy= -sinphi**2.*R2deriv\
-2.*sinphi*cosphi/R**2.*phiforce\
-2.*sinphi*cosphi/R*Rphideriv\
+cosphi**2./R*Rforce\
-cosphi**2./R**2.*phi2deriv
return nu.array([x[2],x[3],
cosphi*Rforce-1./R*sinphi*phiforce,
sinphi*Rforce+1./R*cosphi*phiforce,
x[6],x[7],
dFxdx*x[4]+dFxdy*x[5],
dFydx*x[4]+dFydy*x[5]])
def E(self, *args, **kwargs):
"""
NAME:
E
PURPOSE:
calculate the energy
INPUT:
pot=
t= time at which to evaluate E
OUTPUT:
energy
HISTORY:
2010-09-15 - Written - Bovy (NYU)
"""
if not 'pot' in kwargs or kwargs['pot'] is None:
try:
pot = self._pot
except AttributeError:
raise AttributeError("Integrate orbit or specify pot=")
if 'pot' in kwargs and kwargs['pot'] is None:
kwargs.pop('pot')
else:
pot = kwargs.pop('pot')
if isinstance(pot, Potential):
thispot = toPlanarPotential(pot)
elif isinstance(pot, list):
thispot = []
for p in pot:
if isinstance(p, Potential):
thispot.append(toPlanarPotential(p))
else:
thispot.append(p)
else:
thispot = pot
if len(args) > 0:
t = args[0]
else:
t = 0.
#Get orbit
thiso = self(*args, **kwargs)
onet = (len(thiso.shape) == 1)
if onet:
return _evaluateplanarPotentials(thispot,thiso[0],
phi=thiso[3],t=t)\
+thiso[1]**2./2.\
+thiso[2]**2./2.
else:
return nu.array([_evaluateplanarPotentials(thispot,thiso[0,ii],
phi=thiso[3,ii],
t=t[ii])\
+thiso[1,ii]**2./2.\
+thiso[2,ii]**2./2. for ii in range(len(t))])
def E(self,*args,**kwargs):
"""
NAME:
E
PURPOSE:
calculate the energy
INPUT:
pot=
t= time at which to evaluate E
OUTPUT:
energy
HISTORY:
2010-09-15 - Written - Bovy (NYU)
"""
if not 'pot' in kwargs or kwargs['pot'] is None:
try:
pot= self._pot
except AttributeError:
raise AttributeError("Integrate orbit or specify pot=")
if 'pot' in kwargs and kwargs['pot'] is None:
kwargs.pop('pot')
else:
pot= kwargs.pop('pot')
if isinstance(pot,Potential):
thispot= toPlanarPotential(pot)
elif isinstance(pot,list):
thispot= []
for p in pot:
if isinstance(p,Potential): thispot.append(toPlanarPotential(p))
else: thispot.append(p)
else:
thispot= pot
if len(args) > 0:
t= args[0]
else:
t= 0.
#Get orbit
thiso= self(*args,**kwargs)
onet= (len(thiso.shape) == 1)
if onet:
return _evaluateplanarPotentials(thispot,thiso[0],
phi=thiso[3],t=t)\
+thiso[1]**2./2.\
+thiso[2]**2./2.
else:
return nu.array([_evaluateplanarPotentials(thispot,thiso[0,ii],
phi=thiso[3,ii],
t=t[ii])\
+thiso[1,ii]**2./2.\
+thiso[2,ii]**2./2. for ii in range(len(t))])
def potentialAxi(R,pot,vc=1.,ro=1.):
"""
NAME:
potentialAxi
PURPOSE:
return the potential
INPUT:
R - Galactocentric radius (/ro)
pot - potential
vc - circular velocity
ro - reference radius
OUTPUT:
Phi(R)
HISTORY:
2010-11-30 - Written - Bovy (NYU)
"""
return _evaluateplanarPotentials(pot,R)
