Arbitrary Order Numerical Solutions Conserving the Jacoby Constant in the Motion Near the Equilibrium Points
Abstract
In the paper a modification of the polynomial extrapolation for solving the problem of motion nearby the equilibrium points is presented. It appears that the modification yields a better approximation of the exact solution than the convential polynomial extrapolation and other methods. Moreover, the modification conserves the Jacobi constant of motion. Computer examples for orbits nearby the equilibrium points of the SunJupiter system are given.
 Publication:

Celestial Mechanics
 Pub Date:
 June 1987
 DOI:
 10.1007/BF01230255
 Bibcode:
 1987CeMec..40...95M
 Keywords:

 Celestial Mechanics;
 Hypergeometric Functions;
 Numerical Analysis;
 Orbit Calculation;
 Two Body Problem;
 Computerized Simulation;
 Equations Of Motion;
 Libration;
 Many Body Problem;
 Numerical Integration;
 Orbital Mechanics;
 Astronomy