The regularization of a new problem, namely the three-body problem, using'similar' coordinate system is proposed. For this purpose we use the relationof 'similarity', which has been introduced as an equivalence relation in aprevious paper (see \cite{rom11}). First we write the Hamiltonian function, theequations of motion in canonical form, and then using a generating function, weobtain the transformed equations of motion. After the coordinatestransformations, we introduce the fictitious time, to regularize the equationsof motion. Explicit formulas are given for the regularization in the coordinatesystems centered in the more massive and the less massive star of the binarysystem. The 'similar' polar angle's definition is introduced, in order toanalyze the regularization's geometrical transformation. The effect ofLevi-Civita's transformation is described in a geometrical manner. Using theresulted regularized equations, we analyze and compare these canonicalequations numerically, for the Earth-Moon binary system.
展开▼
