Typical motions in multiple systems

In very old times, people counted - one, two, many. The author wants to show that they were right. Consider the motions of isolated bodies: (1) N = 1 - simple motion; (2) N = 2 - Keplerian orbits; and (3) N = 3 - this is the difficult problem. In general, this problem can be studied only by computer simulations. The author studied this problem over many years (see, e.g., Agekian and Anosova, 1967; Anosova, 1986, 1989 a,b). The principal result is that two basic types of dynamics take place in triple systems. The first special type is the stable hierarchical systems with two almost Keplerian orbits. The second general type is the unstable triple systems with complicated motions of the bodies. By random choice of the initial conditions, by the Monte-Carlo method, the stable systems comprised about approx. 10% of the examined cases; the unstable systems comprised the other approx. 90% of cases under consideration. In N greater than 3, the studies of dynamics of such systems by computer simulations show that we have in general also the motions roughly as at the cases 1 - 3 with the relative negative or positive energies of the bodies. In the author's picture, the typical trajectories of the bodies in unstable triple systems of the general type of dynamics are seen. Such systems are disrupted always after close triple approaches of the bodies. These approaches play a role like the gravitational slingshot. Often, the velocities of escapers are very large. On the other hand, the movie also shows the dynamical processes of a formation, dynamical evolution and disruption of the temporary wide binaries in triples and a formation of final hard massive binaries in the final evolution of triples.