A numerical investigation of the onedimensional Newtonian threebody problem. II  Positive energies
Abstract
Numerical orbit integrations have been conducted to characterize the types of trajectories in the onedimensional Newtonian threebody problem with equal masses and positive energy. At positive energies the basic types of motions are 'binary plus single particle' and 'ionization,' and when time goes from negative to positive infinity all possible transitions between these states can take place. Properties of individual orbits have been summarized in the form of graphical maps in a twodimensional grid of initial values. The basic motion types exist at all positive energies, but the binary plus single particle configuration is obtained only in a narrow region of initial values if the total energy is large. At very large energies the equations of motion can be solved approximately, and this asymptotic result, exact in the limit of infinite energy, is presented.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 1990
 Bibcode:
 1990CeMDA..47..321M
 Keywords:

 Newton Theory;
 Numerical Analysis;
 Three Body Problem;
 Trajectory Analysis;
 Asymptotic Methods;
 Equations Of Motion;
 Orbit Calculation;
 Physics (General)