SOLVABLE (NONRELATIVISTIC, CLASSICAL) N-BODY PROBLEMS ON THE LINE .2.

A solvable n-body problem is exhibited, which features equations of mo tion of Newtonian type, m(j)xdouble over dot(j)=F-j, j=1,...,n, with ' 'forces'' F-j that are linear and quadratic in the particle velocities , F-j=xover dot(j){Sigma(k=1)(n)[f(jk)((1))(x)+xover dot(k)f(jk)((2))( x)]}, and depend highly nonlinearly on the positions x(k)=x(k)(t), k=1 ,...,n, of the n ''particles'' on the line. Explicit expressions of th e functions f(jk)((i))(x), in terms of elliptic functions, are given; they contain n+4 arbitrary constants, in addition to the n ''masses'' m(k) and to n arbitrary functions g(k)(x(k)). Special cases in which t he elliptic functions reduce to trigonometric or rational functions ar e of course included. The technique whereby this model has been arrive d at entails that its initial-value problem is solvable by quadratures [for any n and arbitrary initial data x(0) and xover dot(0)]. A discu ssion of the actual behavior of the solution, and of special cases, is postponed to future papers. (C) 1996 American Institute of Physics.