# Source code for galpy.potential.HenonHeilesPotential

###############################################################################
#   HenonHeilesPotential: the Henon-Heiles (1964) potential
###############################################################################
import numpy
from .planarPotential import planarPotential
[docs]class HenonHeilesPotential(planarPotential):
"""Class that implements a the Henon & Heiles (1964) <http://adsabs.harvard.edu/abs/1964AJ.....69...73H>__ potential

.. math::

\\Phi(R,\\phi) = \\frac{\\mathrm{amp}}{2}\\,\\left[R^2 + \\frac{2\\,R^3}{3}\\,\\sin\\left(3\,\phi\\right)\\right]

"""
[docs]    def __init__(self,amp=1.,ro=None,vo=None):
"""
NAME:

__init__

PURPOSE:

initialize a Henon-Heiles potential

INPUT:

amp - amplitude to be applied to the potential (default: 1.)

OUTPUT:

(none)

HISTORY:

2017-10-16 - Written - Bovy (UofT)

"""
planarPotential.__init__(self,amp=amp,ro=ro,vo=vo)
self.hasC= True
self.hasC_dxdv= True

def _evaluate(self,R,phi=0.,t=0.):
"""
NAME:
_evaluate
PURPOSE:
evaluate the potential at R,phi,t
INPUT:
phi - azimuth
t - time
OUTPUT:
Phi(R,phi,t)
HISTORY:
2017-10-16 - Written - Bovy (UofT)
"""
return 0.5*R*R*(1.+2./3.*R*numpy.sin(3.*phi))

def _Rforce(self,R,phi=0.,t=0.):
"""
NAME:
_Rforce
PURPOSE:
evaluate the radial force for this potential
INPUT:
phi - azimuth
t - time
OUTPUT:
HISTORY:
2017-10-16 - Written - Bovy (UofT)
"""
return -R*(1.+R*numpy.sin(3.*phi))

def _phiforce(self,R,phi=0.,t=0.):
"""
NAME:
_phiforce
PURPOSE:
evaluate the azimuthal force for this potential
INPUT:
phi - azimuth
t - time
OUTPUT:
the azimuthal force
HISTORY:
2017-10-16 - Written - Bovy (UofT)
"""
return -R**3.*numpy.cos(3.*phi)

def _R2deriv(self,R,phi=0.,t=0.):
"""
NAME:
_R2deriv
PURPOSE:
evaluate the second radial derivative for this potential
INPUT:
phi - azimuth
t - time
OUTPUT:
HISTORY:
2017-10-16 - Written - Bovy (UofT)
"""
return 1.+2.*R*numpy.sin(3.*phi)

def _phi2deriv(self,R,phi=0.,t=0.):
"""
NAME:
_phi2deriv
PURPOSE:
evaluate the second azimuthal derivative for this potential
INPUT:
phi - azimuth
t - time
OUTPUT:
the second azimuthal derivative
HISTORY:
2017-10-16 - Written - Bovy (UofT)
"""
return -3.*R**3.*numpy.sin(3.*phi)

def _Rphideriv(self,R,phi=0.,t=0.):
"""
NAME:
_Rphideriv
PURPOSE:
evaluate the mixed radial, azimuthal derivative for this potential
INPUT: