sentences:  Introducing elliptic coordinates,
  
  the potential energy can be written as
  
  and the kinetic energy as
  
  This is a Liouville dynamical system if ξ and η are taken as φ1 and φ2, respectively; thus, the function "Y" equals
  
  and the function "W" equals
  
  Using the general solution for a Liouville dynamical system below, one obtains
  
  Introducing a parameter "u" by the formula
  
  gives the parametric solution
  
  Since these are elliptic integrals, the coordinates ξ and η can be expressed as elliptic functions of "u".The bicentric problem has a constant of motion, namely,
  
  from which the problem can be solved using the method of the last multiplier.To eliminate the "v" functions, the variables are changed to an equivalent set
  
  giving the relation
  
  which defines a new variable "F".