A simple derivation and interpretation of the third integral in Stellar   Dynamics
  Starting from the problem of two fixed centres we find a simple derivation of its third integral in terms of the scalar product of the angular momenta about the two fixed centres. This is then generalised to find the general form of the potential in which an exact third integral exists. 
Donald Lynden-Bell (The Observatories of the Carnegie Institution,   Pasadena, USA, The Institute of Astronomy and Clare Col...