def _external_force(x,t,pot):
dim= len(x)
if dim == 3:
#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= evaluateRforces(R,x[2],pot,phi=phi,t=t)
phiforce= evaluatephiforces(R,x[2],pot,phi=phi,t=t)
return nu.array([cosphi*Rforce-1./R*sinphi*phiforce,
sinphi*Rforce+1./R*cosphi*phiforce,
evaluatezforces(R,x[2],pot,phi=phi,t=t)])
elif dim == 2:
#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(R,pot,phi=phi,t=t)
phiforce= evaluateplanarphiforces(R,pot,phi=phi,t=t)
return nu.array([cosphi*Rforce-1./R*sinphi*phiforce,
sinphi*Rforce+1./R*cosphi*phiforce])
elif dim == 1:
return evaluatelinearForces(x,pot,t=t)
def _rectForce(x,pot,t=0.):
"""
NAME:
_rectForce
PURPOSE:
returns the force in the rectangular frame
INPUT:
x - current position
t - current time
pot - (list of) Potential instance(s)
OUTPUT:
force
HISTORY:
2011-02-02 - 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= evaluateRforces(R,x[2],pot,phi=phi,t=t)
phiforce= evaluatephiforces(R,x[2],pot,phi=phi,t=t)
return nu.array([cosphi*Rforce-1./R*sinphi*phiforce,
sinphi*Rforce+1./R*cosphi*phiforce,
evaluatezforces(R,x[2],pot,phi=phi,t=t)])
def _rectForce(x,pot,t=0.):
"""
NAME:
_rectForce
PURPOSE:
returns the force in the rectangular frame
INPUT:
x - current position
t - current time
pot - (list of) Potential instance(s)
OUTPUT:
force
HISTORY:
2011-02-02 - 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= evaluateRforces(R,x[2],pot,phi=phi,t=t)
phiforce= evaluatephiforces(R,x[2],pot,phi=phi,t=t)
return nu.array([cosphi*Rforce-1./R*sinphi*phiforce,
sinphi*Rforce+1./R*cosphi*phiforce,
evaluatezforces(R,x[2],pot,phi=phi,t=t)])
def _RZEOM(y,t,pot,l2):
"""
NAME:
_RZEOM
PURPOSE:
implements the EOM, i.e., the right-hand side of the differential
equation
INPUT:
y - current phase-space position
t - current time
pot - (list of) Potential instance(s)
l2 - angular momentum squared
OUTPUT:
dy/dt
HISTORY:
2010-04-16 - Written - Bovy (NYU)
"""
return [y[1],
l2/y[0]**3.+evaluateRforces(y[0],y[2],pot,t=t),
y[3],
evaluatezforces(y[0],y[2],pot,t=t)]
def _RZEOM(y, t, pot, l2):
"""
NAME:
_RZEOM
PURPOSE:
implements the EOM, i.e., the right-hand side of the differential
equation
INPUT:
y - current phase-space position
t - current time
pot - (list of) Potential instance(s)
l2 - angular momentum squared
OUTPUT:
dy/dt
HISTORY:
2010-04-16 - Written - Bovy (NYU)
"""
return [
y[1], l2 / y[0]**3. + evaluateRforces(y[0], y[2], pot, t=t), y[3],
evaluatezforces(y[0], y[2], pot, t=t)
]
def _FullEOM(y,t,pot):
"""
NAME:
_FullEOM
PURPOSE:
implements the EOM, i.e., the right-hand side of the differential
equation
INPUT:
y - current phase-space position
t - current time
pot - (list of) Potential instance(s)
OUTPUT:
dy/dt
HISTORY:
2010-04-16 - Written - Bovy (NYU)
"""
l2= (y[0]**2.*y[3])**2.
return [y[1],
l2/y[0]**3.+evaluateRforces(y[0],y[4],pot,phi=y[2],t=t),
y[3],
1./y[0]**2.*(evaluatephiforces(y[0],y[4],pot,phi=y[2],t=t)-
2.*y[0]*y[1]*y[3]),
y[5],
evaluatezforces(y[0],y[4],pot,phi=y[2],t=t)]
def _FullEOM(y,t,pot):
"""
NAME:
_FullEOM
PURPOSE:
implements the EOM, i.e., the right-hand side of the differential
equation
INPUT:
y - current phase-space position
t - current time
pot - (list of) Potential instance(s)
OUTPUT:
dy/dt
HISTORY:
2010-04-16 - Written - Bovy (NYU)
"""
l2= (y[0]**2.*y[3])**2.
return [y[1],
l2/y[0]**3.+evaluateRforces(y[0],y[4],pot,phi=y[2],t=t),
y[3],
1./y[0]**2.*(evaluatephiforces(y[0],y[4],pot,phi=y[2],t=t)-
2.*y[0]*y[1]*y[3]),
y[5],
evaluatezforces(y[0],y[4],pot,phi=y[2],t=t)]