def meanOmega(self,dangle,oned=False,tdisrupt=None,approx=True,
                  higherorder=None):
        """
        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)

        """
        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
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)