Improved criteria for hyperbolic-elliptic motion in the general three-body problem, 2

Abstract In addition to the previous criteria (YOSHIDA 1972) for the hyperbolic-elliptic motion in the general three-body problem, another one is given by taking into account the non-zero angular momentum. So long as the conditions regarding the angular momentum of the system are satisfied, the new criterion includes theorem 1 in YOSHIDA (1972). The effect of the new criterion is different in each case as illustrated in BECKER's (1920) numerical examples, having a negative total energy. In disregard of the rigorous estimations of numerical errors, these examples are shown to be hyperbolic-elliptic as t → +∞, and thus contradict CHAZY's (1929) assertion that there are no motions of the exchange type in the three-body problem.