Article · Programming and Computer Software · September 1, 2017
Investigation of the restricted problem of three bodies of variable masses using computer algebra
Alexander N. Prokopenya, M. Zh. Minglibayev, G. M. Mayemerova, Zh. U. Imanova
Abstract
The classical restricted three-body problem for bodies with variable masses is discussed for the case when the masses of two bodies vary isotropically at different rates and their sum varies according to the joint Meshchersky law. Within the perturbation theory in Hills’s approximation, differential equations determining the secular perturbations of the orbital elements are obtained and it is shown that they are integrable under arbitrary laws governing the mass variations satisfying the joint Meshchersky law. The influence of the variations of the body masses on the evolution of the orbital parameters is comparable with the perturbations created by massive bodies. All symbolic computations are performed in Wolfram Mathematica .
More by Mukhtar Minglibayev
- DIFFERENTIAL MOTION EQUATIONS OF THE VARIABLE-MASS THREE-BODY PROBLEM WITH REACTIVE FORCES IN A BARYCENTRIC COORDINATE SYSTEMJournal of Mathematics Mechanics and Computer Science · 2026
- Secular Perturbations of Translational–Rotational Motion of an Axisymmetric Body in the Restricted Three-Body Problem with Variable MassesAxioms · 2026
- The equation of motion for the variable mass TRAPPIST-1 exoplanet system in the Jacobi coordinate systemBulletin of the National Engineering Academy of the Republic of Kazakhstan · 2026
- EXACT SOLUTIONS OF EQUATIONS OF THE TWO-PRIMARY-BODY PROBLEM IN THE RESTRICTED THREE-BODY PROBLEM WITH VARIABLE MASSESJournal of Mathematics Mechanics and Computer Science · 2025