A computer aided analysis of the Sitnikov problem
We deal with the problem of a zero mass body oscillating perpendicular to a plane in which two heavy bodies of equal mass orbit each other on Keplerian ellipses. The zero mass body intersects the primaries plane at the systems barycenter. This problem is commonly known as the Sitnikov problem. In this work we are looking for a first integral related to the oscillatory motion of the zero mass body. This is done by expressing the equation of motion by a second order polynomial differential equation using a Chebyshev approximation techniques. We search for an autonomous mapping of the canonical variables over one period of the primaries. In addition, we present a detailed analysis of the linearized Sitnikov problem which is valid for infinitesimally small oscillation amplitudes of the zero mass body. All computations are performed automatically by the FORTRAN program SALOME which has been designed for stability considerations in high energy particle accelerators.
second order polynomial differential equation
scientific article; zbMATH DE number 429318