Solvable and/or integrable and/or linearizable N-body problems in ordinary(three-dimensional) space. I

Several N-body problems in ordinary (3-dimensional) space are introduced wh ich are characterized by Newtonian equations of motion (acceleration equal force; in most cases, the forces are velocity-dependent) and are amenable t o exact treatment (solvable and/or integrable and/or linearizable). These e quations of motion are always rotation-invariant, and sometimes translation -invariant as well. In many cases they are Hamiltonian, but the discussion of this aspect is postponed to a subsequent paper. We consider few-body pro blems (with, say, N = 1,2,3,4,6,8,12,16,...) as well as many-body problems (N an arbitrary positive integer). The main focus of this paper is on vario us techniques to uncover such N-body problems. We do not discuss the detail ed behavior of the solutions of all these problems, but we do identify seve ral models whose motions are completely periodic or multiply periodic, and we exhibit in rather explicit form the solutions in some cases.