Multinomialization of the Classical Three Body Problem Before Applying Probabilistic Evolution Approach

Abstract

This work aims to reshape the equation of motion for a celestial mechanical three body problem for an efficient application of the recently developed Probabilistic Evolution Approach (PEA) for explicit ODEs. It is well known that the multinomiality in descriptive functions facilitates the construction of the truncation approximants. In case of nonexistence, the multinomiality can be obtained by using the space extension method at the expense of an increase in the number of the unknowns and may bring block triangularity which is another important facility to investigate and control the properties of PEA. Before proceeding with space extension we construct the Hamilton equations of motion for the system first and then define new appropriate unknown functions depending on the existing unknowns such that the resulting ODEs to be used in PEA become multinomials. This attempt provides us with block triangularity at the same time.