code: def meanOmega(self,dangle,oned=False,tdisrupt=None,approx=True,
                    higherorder=None):
          
          if higherorder is None: higherorder= self._higherorderTrack
          if tdisrupt is None: tdisrupt= self._tdisrupt
          if approx:
              num= self._meanOmega_num_approx(dangle,tdisrupt,
                                              higherorder=higherorder)
          else:
              num=\
                  integrate.quad(lambda T: (T/(1-T*T)\
                                                *numpy.sqrt(self._sortedSigOEig[2])\
                                                +self._meandO)\
                                     *numpy.sqrt(self._sortedSigOEig[2])\
                                     *(1+T*T)/(1-T*T)**2.\
                                     *self.pOparapar(T/(1-T*T)\
                                                         *numpy.sqrt(self._sortedSigOEig[2])\
                                                         +self._meandO,dangle),
                                 -1.,1.)[0]
          denom= self._density_par(dangle,tdisrupt=tdisrupt,approx=approx,
                                   higherorder=higherorder)
          dO1D= num/denom
          if oned: return dO1D
          else:
              return self._progenitor_Omega+dO1D*self._dsigomeanProgDirection\
                  *self._sigMeanSign
docs: NAME:
  
             meanOmega
  
          PURPOSE:
  
             calculate the mean frequency as a function of angle, assuming a uniform time distribution up to a maximum time
  
          INPUT:
  
             dangle - angle offset
  
             oned= (False) if True, return the 1D offset from the progenitor (along the direction of disruption)
  
             approx= (True) if True, compute the mean Omega by direct integration of the spline representation
  
             higherorder= (object-wide default higherorderTrack) if True, include higher-order spline terms in the approximate computation
  
          OUTPUT:
  
             mean Omega
  
          HISTORY:
  
             2015-11-17 - Written - Bovy (UofT)